Election Live Updates: Vance in Arizona to Discuss Border as Walz Stumps in Pennsylvania

Vice President Kamala Harris’s running mate, Gov. Tim Walz of Minnesota, is in Pennsylvania with his daughter, Hope. The two are set to appear soon at a rally in Erie. Pennsylvania has emerged as a must-win battleground in the presidential election, and both campaigns are swarming it this week. Ms. Harris stumped in Pittsburgh earlier on Thursday, a day after Mr. Trump appeared at a town-hall event in Harrisburg hosted by Fox News.

Here’s what else to know:

• Courting business: Mr. Trump called for the creation of a government efficiency commission during a speech in New York on Thursday, adopting a policy idea that was pitched to him by the billionaire businessman Elon Musk. His remarks came a day after Ms. Harris reached out to the business community, rolling out a series of economic proposals in New Hampshire that marked her biggest policy move away from President Biden yet.

• Trump and Jewish voters: He addressed a meeting of the Republican Jewish Coalition, a group of prominent Jewish Republican political donors, on Thursday, highlighting his Israel policies and repeating his criticisms of Jewish Americans who support Democrats.

• Harris-Trump debate: On Tuesday, Ms. Harris and Mr. Trump will meet in Philadelphia for their first presidential debate, to be hosted by ABC News. The consequential matchup may attract tens of millions of viewers. The network on Wednesday announced the rules the campaigns had agreed to, which, as in Mr. Trump’s debate with President Biden, include no live audience and a muted microphone when the other candidate is speaking.

• Misinformation on voting: Republicans are seizing on false theories about voting by immigrants. Activists, party lawyers and state officials are mobilizing behind a crackdown on what they have baselessly claimed is a scourge of noncitizens casting ballots. Voting rights advocates say the effort is spreading misinformation.

• Cheney for Harris: Former Representative Liz Cheney of Wyoming, a once high-ranking Republican who has emerged as an outspoken Trump critic, said on Wednesday that she would vote for Ms. Harris. Her support could help the Harris campaign as it ramps up appeals to Republican voters disaffected with Mr. Trump.

• Walz family feud: Distant relatives of the governor came out in support of Mr. Trump. Mr. Walz’s sister, Sandy Dietrich, said that they weren’t close to that side of the family. But Mr. Walz’s brother, Jeff Walz, has donated to Mr. Trump and said he was “100 percent opposed” to the governor’s views.

• Sept. 11 memorials: Mr. Biden and Ms. Harris are set to visit the World Trade Center site in New York City on Sept. 11 to memorialize victims of the 2001 terrorist attacks. Mr. Trump is considering doing so.

“In the words of a great but highly underrated president, William McKinley, highly underrated, the protective tariff policy of the Republicans has been made — and made — the lives of our countrymen sweeter and brighter,” he said on Thursday during a rambling speech billed as a major economic address.

Mr. Trump seemed aware that his prescriptions for import tariffs on every product made abroad and a preferential 15 percent corporate tax rate for domestic manufacturers might not resonate in the high temple of global finance.

“You can call it what you want; some might say it’s economic nationalism,” he said after name-checking some of Wall Street’s richest men, such as Stephen A. Schwarzman, the chief executive of the Blackstone Group, Jamie Dimon, the chief executive of JPMorgan Chase, and John Paulson, the famed hedge fund manager. “I call it common sense. I call it America First. This is the policy that built this country, and this is the policy that will save our country.”

His solution for the deficit? Tariffs. The crisis for middle-class families struggling with child care? The economic growth he said would be spurred by things like tariffs. A complicated international supply chain that has the wings of military aircraft manufactured in one country and the tail in another? Tariffs.

The promised growth would even finance the creation of a sovereign wealth fund, a government-run investment entity common in countries like Saudi Arabia and Norway awash in petrodollars, not in a nation like the United States, where the federal deficit reached $1.7 trillion last fiscal year.

(The other answer is harsh immigration policies, he said: cutting off all assistance to undocumented immigrants to lower the deficit, followed by their mass deportation, which would open up homes and lower housing costs.)

If the economic minds of Wall Street looked askance at these ideas, they did not immediately say it. Vice President Kamala Harris tried to come their way on Wednesday by lowering her prescribed top capital gains tax rate for the wealthy to 28 percent, rather than the 39.6 percent rate that President Biden wanted, which would have taxed investment income at the same rate as earned income.

But Mr. Trump was promising them even lower taxes: a full extension of the tax cuts he won in 2017 that heavily favored the rich — and even more, such as the ability to write business investment fully off the corporate balance sheet. That has been good enough to keep some of the wealthiest Americans in Mr. Trump’s camp.

After the speech, Mr. Paulson applauded the former president’s ideas. “What Trump would like to do is restore American manufacturing again, make America a manufacturing powerhouse, and that would benefit our economy,” he said in an interview. “That would give us strategic value and benefit workers — and tariffs are a tool to achieve that.”

More traditional economists — and Democrats — are not so sanguine. Lawrence Summers, a Treasury secretary in the Clinton administration, has said that Mr. Trump’s policies would stifle international competition, raise consumer costs and increase corporate profits at the expense of falling inflation-adjusted wages in the American work force.

Jared Bernstein, the chairman of President Biden’s White House Council of Economic Advisers, said after the speech, “Virtually every economist has come to the same conclusion: Trump’s proposed huge increase in tariffs will constitute a massive new sales tax on the middle class and will reverse the significant progress we’ve made against inflation.”

Mr. Trump took time in the speech to take aim at Ms. Harris, saying at one point that “as everyone knows, she is a Marxist.”

But not all Marxism is bad in his telling, apparently: “China was built on doing exactly what we’re going to be doing,” he said.

If China had five-year plans and the Great Leap Forward, Mr. Trump had prescriptions that were a little more vague. At one point, he did nod to the future — “A.I., controversial,” he said, “but we got to be the top of it.”

Yet he spent more time on the wonders of the past, without acknowledging how much has changed since 1890, when McKinley, as a U.S. Representative, drafted the law that raised import tariffs by 50 percent to protect American industry, and 1901, when McKinley, as president, was assassinated.

“Teddy Roosevelt became a great president, spending the money that was made by McKinley,” Mr. Trump said.

Mr. Trump did marvel at one technology, nuclear power, as he talked of John Trump, his uncle who was a professor at the Massachusetts Institute of Technology.

“We used to talk about it,” Mr. Trump said, “and I’d say, ‘Uncle John, there’s no way.’ He was telling me about this incredible power that was being unleashed potentially. And I’d say, ‘Uncle John, you could never.’”

Needless to say, Mr. Trump would like a lot more nuclear power.

President Biden, during a speech on clean energy investments in Wisconsin, expressed some regret over the branding of his signature climate bill, the Inflation Reduction Act. The bill includes billions of dollars of funding for clean energy investments but has little to do with driving down inflation — Democrats, however, named it that way to address concerns over rising prices, a major political vulnerability.

“The most significant climate change law ever and by the way,” Biden said. “We should’ve named it what it was but any rate.” His acknowledgement comes as he pitches Vice President Kamala Harris to be his successor and tries to find an effective way to sell their administration’s economic and climate investments — something his White House has failed to accomplish consistently.

Gov. Tim Walz of Minnesota and his daughter, Hope, are set to appear at a rally this evening in Erie, Pa. The city sits in a working-class county that was once reliably Democratic but became a critical swing region after former President Donald J. Trump won it in 2016, when many voters were swayed by his promises to rebuild American manufacturing.

Here’s what we know.

What was said

“He signed legislation, he supported legislation, that would take children away from their parents if their parents don’t want to do sex changes.”

“He wants the government to steal your children from you if you don’t agree with Tim Walz’s values. That is not small government. That is disgusting, and he should be ashamed of himself.”
— Mr. Vance said at an event hosted by the conservative group Turning Point Action in Mesa, Ariz.

This is false. Since Mr. Walz was picked as Vice President Kamala Harris’s running mate, conservative groups, including the Alliance Defending Freedom — the conservative Christian legal advocacy group — have claimed that the Minnesota state authorities can terminate the parental rights of parents who prevent their children from receiving gender-affirming care. A spokeswoman for Mr. Vance cited the alliance’s arguments to support his claim.

But those groups have been unable to name a case in which that has happened, pointing instead to hypothetical scenarios about a provision in the law that grants Minnesota courts “temporary emergency jurisdiction” during custody disputes crossing state lines if a child “has been unable to obtain gender-affirming health care.”

PolitiFact, citing legal experts and family law practitioners in Minnesota, concluded that the law “does not authorize the government to take custody of children whose parents don’t consent to them getting gender-affirming care.”

In a response to The New York Times, Taylor Van Kirk, a spokeswoman for Mr. Vance, disputed The Times’s conclusion but failed to provide evidence with which to refute it, instead repeating Mr. Vance’s false contention that the law “would allow for children to be removed from the custody of their parents.’”

Some of the provisions of an executive order that Mr. Walz signed protected the parents of transgender children, preventing the state from enforcing subpoenas and judgments from other states meant to punish transgender care. Rather than giving the state the power to terminate parental rights, the executive order prevents other states from terminating parental rights solely on the basis of a parent’s providing gender-affirming care to their child.

Mr. Vance’s remarks about transgender children, which earned some of the strongest applause of his appearance in Arizona, came just days after former President Donald J. Trump made a similar false claim that schools are secretly providing gender-affirming surgeries for transgender children against the will of their parents.

“The transgender thing is incredible,” Mr. Trump said on Friday at a gathering of the conservative group Moms for Liberty. “Think of it. Your kid goes to school and comes home a few days later with an operation. The school decides what’s going to happen with your child.”

The Trump campaign and conservative organizations did not provide any evidence to support that claim to CNN for a fact check, while medical experts also told CNN that the claim was false.

Michael Gold contributed reporting.

About two hours after Donald J. Trump suggested he would limit the use of sanctions in a speech to the Economic Club of New York, he celebrated the sanctions he imposed on Iran in a live-via-satellite speech to a gathering of the Republican Jewish Coalition. Trump earlier suggested tariffs might be a more effective tool for influencing other nations than sanctions.

Trump, pointing to his Israel policies, has said several times that Jewish Americans were safer under his administration and repeated that Jewish Americans who back Democrats need “to have your head examined.” But the Anti-Defamation League noted a rise in reported antisemitic incidents in the United States during Trump’s administration, and Trump was criticized during his presidency for not directly addressing the violence and rhetoric of white supremacists, some of whom were his supporters.

Trump just promised to eliminate a minimum of 10 existing government regulations for every new regulation added under his administration if he is elected. He also said he would create a “government efficiency commisson” that will “eliminate fraud and improper payments.” Both proposals, he said, will reduce government spending and lower prices for American consumers.

Trump also pledged to reduce the corporate tax rate from 21 percent to 15 percent but “solely for companies that make their products in America.” And he vowed to expand tariffs on companies that import their products from overseas. Trump previously cut the corporate tax rate from 35 percent to 21 percent. Harris has proposed raising it to 28 percent.

In a wide-ranging and sometimes meandering speech that lasted more than an hour, Mr. Trump recast his first-term record as an economic miracle and renewed his pitch for lowering taxes and raising tariffs on imports, often disregarding some of the potential implications of his new proposals.

The trade wars that Mr. Trump started had painful consequences for American farmers, and the new tariffs that he called for would also likely trigger backlash and retaliation from other countries. Mr. Trump claimed that his new tax cuts would be paid for by spurring economic growth, but the 2017 tax cuts he enacted increased the national debt and his growth projections never panned out.

Mr. Trump’s embrace of the concept of a government efficiency commission — a favorite Washington solution for delaying dealing with hard problems — comes as he is trying to define how his stewardship of the economy would differ from that of his Democratic opponent, Vice President Kamala Harris. He has assailed her economic vision as one that would saddle the economy with wasteful spending and burdensome regulations.

During his speech, Mr. Trump also vowed to eliminate 10 existing government regulations for every new regulation added under his potential new administration. Mr. Trump — who during his presidency issued an executive order vowing a similar two-for-one rule — argued that the cost of regulations was being passed onto consumers.

Trump advisers said it was not yet clear how a government efficiency commission would be staffed. But having Mr. Musk lead such a commission could pose potential conflicts of interest. His rocket company, SpaceX, has contracts from the federal government. And his car company, Tesla, has benefited from tax credits and government incentives meant to spur the production and adoption of electric vehicles.

Mr. Trump, in his address to the Economic Club of New York on Thursday, also made the case for a repeal of the Inflation Reduction Act of 2022, which was President Biden’s signature climate and tax legislation.

On tax policy, Mr. Trump said that he would lower the corporate tax rate to 15 percent from 21 percent. However, companies would be eligible for that reduction, he said, only if they make their products in the United States.

Mr. Trump previously cut the rate from 35 percent in 2017. Ms. Harris has proposed raising it to 28 percent.

And on trade, Mr. Trump signaled that another aggressive round of protectionist measures would be in store for companies that do not produce their goods in the U.S. He branded these “smart tariffs” as a way to shield domestic industries from foreign competition, and insisted that they would not fuel inflation.

Mr. Trump has previously called for imposing a 10 to 20 percent tariff on most imports, as well as a more than 60 percent tariff on Chinese products. He suggested on Thursday that the tariff rates could be higher than what he has proposed.

“We will be bringing in billions and billions of dollars, which will directly reduce our deficits,” Mr. Trump said.

Building on his frequent promise to boost domestic energy production, Mr. Trump said he would declare a national emergency to help cut through bureaucratic regulations and boost drilling for oil, new pipelines and new power plants. American oil and gas production has hit record levels under Mr. Biden, but Mr. Trump said that it would be “four times higher” had he been elected in 2020.

Joseph Costello, a Harris campaign spokesman, criticized Mr. Trump’s economic plans, pointing to reports by experts that have suggested his tariffs would raise costs for consumers rather than lower them. “His agenda will shrink the economy, crush job growth, raise taxes on the middle class, drive up inflation, and explode the national debt,” Mr. Costello said in a statement.

Mr. Trump had previously discussed the idea of an efficiency commission but he stopped short of saying he would adopt it, in a live-streamed conversation with Mr. Musk last month on X, the entrepreneur’s social-media platform.

Though Mr. Musk was once a strong supporter of Democrats and a vocal Trump skeptic, he has grown closer with Mr. Trump as his own politics have shifted. As the tech billionaire became more conservative, Mr. Trump and his team began courting his support.

Mr. Musk endorsed Mr. Trump in July, just hours after Mr. Trump survived an assassination attempt at a rally in Pennsylvania. Their closeness led to Mr. Trump’s return to X, which was formerly Twitter and was long Mr. Trump’s favored social-media platform before he was barred in 2021 and launched a competitor.

Mr. Trump has a tendency to divert any policy-focused speech toward his talking points from his rallies. He veered at times on Thursday to criticize the Biden administration’s withdrawal from Afghanistan, to accuse Ms. Harris of leftist policies on policing and immigration and to stoke fear around migrants and crime.

His speech included some of his frequent false claims, including his assertion that all the job growth during the Biden presidency had gone to undocumented immigrants.

Still, the crowd at Thursday’s speech was more disciplined than the audience at a typical Trump rally. Hundreds of men and women in business attire gathered inside Cipriani’s cavernous bank-turned-banquet hall on East 42nd Street, seated at round tables dressed with white linens.

The audience included many former members of Mr. Trump’s administration, including Steven Mnuchin, his Treasury secretary; Wilbur Ross, his commerce secretary; and Robert Lighthizer, the trade adviser. Financial leaders — Jamie Dimon, the chief executive of JP Morgan; John Paulson, the hedge fund investor; and Stephen A. Schwarzman, the chief executive of Blackstone — were also in attendance.

After his speech, Mr. Trump took four questions from members of the Economic Club. Reshma Saujani, the founder of both Moms First and Girls Who Code, asked Mr. Trump what legislation he might prioritize to address rising child care costs.

In a jumbled answer, Mr. Trump said he would commit to legislation but did not offer any specifics, insisting that his other economic policies, including tariffs, would “take care” of child care. “As much as child care is talked about as being expensive, it’s, relatively speaking, not very expensive compared to the kind of numbers we’ll be taking in,” Mr. Trump said.

Ms. Harris’s campaign, in a statement, called Mr. Trump’s economic plan an effective “tax hike on middle class families” that would not make child care more affordable.

Mr. Trump was also asked how he might alter existing economic sanctions, particularly on Russia.

Acknowledging that he had imposed some during his presidency, Mr. Trump said he would aim to “use sanctions as little as possible” in a bid to avoid other countries turning to Chinese currency. Though he has often cited the sanctions he imposed on Iran as a signature policy achievement, Mr. Trump also suggested that he believed the Biden administration was leaving existing sanctions on other countries in place for too long.

President Vladimir Putin of Russia weighed in on the American election this morning with what appeared to be his usual sarcasm as he spoke on a panel in the Russian city of Vladivostok. Because President Biden has endorsed Vice President Kamala Harris, he said, “we will do the same and support her,” before adding: “The choice is up to the American people.”

In fact, American spy agencies have assessed that the Kremlin favors former President Donald Trump in November. Echoing Trump, Putin also took a jab at Harris’s laugh: “She laughs so expressively and infectiously that it means she’s doing well.” If Harris is doing well, then “maybe she will refrain” from enacting new sanctions against Russia, he added.

Gov. Tim Walz of Minnesota, the Democratic vice-presidential nominee, grew up in Nebraska and still has family there. The photo looks authentically Nebraskan.

It turns out the family is related to Mr. Walz. But they are distant relatives. They are descendants of Francis Walz, the brother of Mr. Walz’s grandfather.

Sandy Dietrich, Tim Walz’s sister, made it clear the two branches of the family were not close.

“That is not us,” Ms. Dietrich, who lives in Alliance, Neb., said in an interview. “We don’t even know them. We just have never known that side” of the family.

The members of Francis Walz’s family told The Associated Press in a written statement that shortly after Mr. Walz was nominated, family members had a get-together.

“We had T-shirts made to show support for President Trump and JD Vance and took a group picture,” the written statement said. “That photo was shared with friends, and when we were asked for permission to post the picture, we agreed.”

“The picture is real. The shirts are real,” the message continued. “The message on the shirts speaks for itself.”

For her part, when asked if she was voting for her brother, Ms. Dietrich said, “I’m a Democrat, so yes, most definitely.”

But even among Mr. Walz’s siblings, there’s a political rift. Mr. Walz’s other sibling, Jeff Walz, has donated to Mr. Trump and comments on Facebook indicate he will not vote for his own brother’s ticket. “I’m 100% opposed to all his ideology,” read a message from his Facebook account.

When a commenter suggested he get onstage with President Trump, the response from Jeff Walz’s account read, “I’ve thought hard about doing something like that. I’m torn between that and just keeping my family out of it.”

Pointing to Vice President Kamala Harris’s longtime friendship with a senior executive whose portfolio includes ABC News, Mr. Trump insisted without evidence that Ms. Harris was “going to get the questions in advance.” The network released agreed-upon rules that no topics or questions would be provided to either candidate or campaign.

Mr. Trump’s attempts to question the integrity of the debate echoed a similar effort that preceded his consequential debate in June with President Biden that set off the president’s exit from the race. After taunting Mr. Biden into debating “anytime, anywhere, anyplace,” Mr. Trump sought to play down any potential political consequences as the debate neared by casting the network, moderators and rules as biased.

“Beyond the debate rules published today, which were mutually agreed upon by two campaigns on May 15th, we have made no other agreements,” an ABC News spokeswoman said on Wednesday night. “We look forward to moderating the presidential debate next Tuesday.”

Yet even as he suggested the debate next week would be biased against him, Mr. Trump also tried to present himself as unconcerned about his first head-to-head confrontation with Ms. Harris since she became the Democratic nominee. He insisted that planning would only get him so far and that he would take a similar approach to Ms. Harris that he did to Mr. Biden.

“I let him talk — I’m going to let her talk,” Mr. Trump told the town hall’s moderator, the Fox News host Sean Hannity. Mr. Trump, who has repeatedly mocked Ms. Harris’s intelligence and speaking style, added, “There are those that say that Biden is smarter than she is. If that’s the case, we have a problem.”

Mr. Trump’s town hall, in front of an audience in Harrisburg, Pa., began with an interview by Mr. Hannity, a longtime Trump ally with whom the former president has a yearslong friendship. Mr. Trump then answered five prescreened questions from members of the audience, including the state’s Republican Senate candidate, David McCormick. The interview portion was broadcast on Fox News on Wednesday evening, and the audience questions are set to run on Thursday evening.

For the bulk of his speaking time, Mr. Trump repeated talking points from his rallies though he occasionally expanded on them.

As he often does, Mr. Trump cited the praise of Hungary’s far-right prime minister, Viktor Orban, whom critics have said has been leading his nation toward authoritarianism, as proof that world leaders preferred his leadership on foreign affairs to Mr. Biden’s.

Describing Mr. Orban as a “strongman,” Mr. Trump, who has praised contemporary strongmen leaders and whose violent and authoritarian rhetoric on the campaign trail has raised alarm from his critics, added, “sometimes you need a strongman.”

As Mr. Trump sat in Pennsylvania, a large producer of natural gas, he vowed to increase oil and gas production, then again attacked Ms. Harris for calling for a ban on hydraulic fracturing, or fracking, during her 2020 presidential campaign.

Though Ms. Harris has since said she no longer supports such a ban, Mr. Trump said that Pennsylvania “can’t take the chance.” Both campaigns are eyeing the battleground state as critical to their paths to victory in November.

Mr. Trump continued to insist that other countries were deliberately sending violent criminals and mentally ill people across the border, a claim that there is no evidence to support, and he accused Ms. Harris of failing to curb the number of migrants crossing illegally.

“She was the border czar,” Mr. Trump said, using a misleading phrase that Republicans have used to describe Ms. Harris’s role in being asked to address the “root causes” of migration.

Then, acknowledging that Ms. Harris was never formally given that title, Mr. Trump added that “even if you don’t want to use that term, she was in charge of the border.”

Mr. Trump also spent significant time looking backward to when Mr. Biden was his opponent. Ms. Harris had visited New Hampshire on Wednesday, and Mr. Trump criticized Mr. Biden over his role in the Democratic National Committee’s decision to move the state from the top of the Democrats’ primary calendar.

“Who the hell in New Hampshire would vote for this guy?” he asked, even though Mr. Biden will no longer be on the ballot there in November.

Mr. Trump’s town hall was meant to stand in for a debate that he had proposed on Fox News as part of an effort to pull out of the ABC News debate he had initially agreed to with Mr. Biden. The Harris campaign rejected his proposal and insisted Mr. Trump uphold his commitment to the ABC debate, which will take place next Tuesday in Philadelphia. Mr. Trump has also proposed a debate on NBC News later this month, which Ms. Harris has so far not agreed to.

The town hall on Fox was part of a larger attempt by the Trump campaign to attack Ms. Harris for avoiding media scrutiny. Mr. Trump and his allies have criticized her commitment to only one debate, her not holding a news conference since becoming the Democratic presidential nominee and her decision to wait a month before giving a mainstream media interview.

Though she took part in an interview last week on CNN, Trump allies have criticized her for fielding it alongside her running mate, Gov. Tim Walz of Minnesota.

Michael M. Grynbaum contributed reporting.

“I don’t believe we have the luxury of writing in candidates’ names, particularly in swing states,” Ms. Cheney said, speaking to students in the hotly contested state of North Carolina. “As a conservative, as someone who believes in and cares about the Constitution, I have thought deeply about this and because of the danger that Donald Trump poses, not only am I not voting for Donald Trump, but I will be voting for Kamala Harris.”

The room erupted in cheers after she made her unexpected announcement.

The decision by Ms. Cheney, whose endorsement Ms. Harris’s campaign had been courting for weeks, to shift from condemning Mr. Trump to backing the Democratic presidential nominee was a striking one even from a leader who has established herself as one of the most vocally anti-Trump Republicans in the country.

In an interview with Fox News in August of 2020, after President Biden selected Ms. Harris as his running mate, Ms. Cheney described his pick as someone “whose voting record in the Senate is to the left of Bernie Sanders and Elizabeth Warren.” She added: “It’s very clear, she is a radical liberal.”

Ms. Cheney, a daughter of former Vice President Dick Cheney, is a member of a private and deeply conservative political family. She is pro-gun and anti-abortion and favors a stronger national defense.

Ms. Harris’s top aides had said they were not certain whether Ms. Cheney, who shares few policy positions with the vice president, would go a step further and make an outright endorsement of the vice president, or simply spend the time between now and Election Day laying out the case against Mr. Trump.

That is the route that some other prominent Republicans have chosen. On Tuesday, Pat Toomey, the ultraconservative former Republican senator from Pennsylvania, said he would not be supporting Mr. Trump in the fall, but he said he could not vote for Ms. Harris, either.

“When you lose an election and you try to overturn the results so that you can stay in power, you lose me — you lose me at that point,” Mr. Toomey told CNBC. “It is an acceptable position for me to say that neither of these candidates can be my choice for president.”

Conservative voices like Mr. Toomey’s could encourage some Republican voters to simply write in a candidate or refrain from voting rather than feeling obligated to vote for their party’s nominee, hurting Mr. Trump’s candidacy.

But Ms. Cheney explicitly rejected Mr. Toomey’s approach, potentially creating a model for deeply conservative voters reluctant to back Mr. Trump to pull the lever for a Democrat for the first time in their lives.

It was her latest break with the Republican Party after losing her leadership position and then her seat for condemning Mr. Trump after the Jan. 6, 2021, attack on the Capitol and voting to impeach him for inciting insurrection. She spent her final months in Congress serving on the special House committee that investigated the assault, and has continued to speak out forcefully against Mr. Trump and make the case publicly that he is a threat to the republic.

Her endorsement was an important show of support for Ms. Harris, who has been pouring tens of millions of dollars into a paid media campaign targeting anti-Trump Republicans. Her campaign has hired a full-time national Republican engagement director and featured Republicans onstage at the nominating convention last month.

But Ms. Cheney had remained silent until now. She chose not to speak at the Democratic National Convention, making the decision to wait for a stand-alone moment in September, closer to when early voting was set to begin.

It was a strategic choice to ensure her voice would not be lost in a sea of convention speeches, according to people familiar with her thinking.

In a series of upcoming appearances in key states, Ms. Cheney plans to make plain the practical implications of a second Trump term, talking with specificity about his abuse of the intelligence community and his attempt to corrupt the Justice Department.

The former Wyoming congresswoman plans to talk about Mr. Trump’s pressure campaign against his vice president to throw out the results of the 2020 presidential election.

Students in the audience on Wednesday night were excited to be in the room where her announcement happened.

“I was conservative when I was younger,” said Ari Miller, who serves as the co-president of Duke Democrats. “I celebrated Trump’s win in 2016 in sixth grade. My first presidential ballot this November will be cast for Harris.”

She said Ms. Cheney’s surprise announcement hit home for her. “I commend Liz Cheney for saying what many Republican leaders won’t. I hope Kamala Harris will consider her for a cabinet position when she is elected in November.”