WASHINGTON — It was one thing in 2016 for top Republicans to take a stand against Donald J. Trump for president: He wasn’t likely to win anyway, the thinking went, and there was no ongoing conservative governing agenda that would be endangered.

The 2020 campaign is different: Opposing the sitting president of your own party means putting policy priorities at risk, in this case appointing conservative judges, sustaining business-friendly regulations and cutting taxes — as well as incurring the volcanic wrath of Mr. Trump.

But, far sooner than they expected, growing numbers of prominent Republicans are debating how far to go in revealing that they won’t back his re-election — or might even vote for Joseph R. Biden Jr., the presumptive Democratic nominee. They’re feeling a fresh urgency because of Mr. Trump’s incendiary response to the protests of police brutality, atop his mishandling of the coronavirus pandemic, according to people who spoke on the condition of anonymity to disclose private discussions.

Former President George W. Bush won’t support the re-election of Mr. Trump, and Jeb Bush isn’t sure how he’ll vote, say people familiar with their thinking. Senator Mitt Romney of Utah won’t back Mr. Trump and is deliberating whether to again write in his wife, Ann, or cast another ballot this November. And Cindy McCain, the widow of Senator John McCain, is almost certain to support Mr. Biden but is unsure how public to be about it because one of her sons is eying a run for office.

None of them voted for Mr. Trump in 2016, but the reproach of big Republican names carries a different weight when an incumbent president and his shared agenda with Senate leaders are on the line.

Former Republican leaders like the former Speakers Paul D. Ryan and John A. Boehner won’t say how they will vote, and some Republicans who are already disinclined to support Mr. Trump are weighing whether to go beyond backing a third-party contender to openly endorse Mr. Biden. Retired military leaders, who have guarded their private political views, are increasingly voicing their unease about the president’s leadership but are unsure whether to embrace his opponent.

Mr. Biden himself, while eager to win support across party lines, intends to roll out his “Republicans for Biden” coalition later in the campaign, after fully consolidating his own party, according to Democrats familiar with the campaign’s planning.

The public expressions of opposition to Mr. Trump from parts of the Republican and military establishment have accelerated in recent days over his repeated calls for protesters to be physically constrained, “dominated,” as he put it, and his administration’s order to forcefully clear the streets outside the White House so he could walk out for a photo opportunity. His conduct has convinced some leaders that they can no longer remain silent.

Former Defense Secretary Jim Mattis’s blistering criticism of Mr. Trump and the admission this week by Senator Lisa Murkowski of Alaska that she is “struggling” with whether to vote for the sitting president of her own party have intensified the soul-searching taking place, forcing a number of officials to reckon with an act that they have long avoided: stating out loud that Mr. Trump is unfit for office.

“This fall, it’s time for new leadership in this country — Republican, Democrat or independent,” said William H. McRaven, the retired Navy admiral who directed the raid that killed Osama bin Laden. “President Trump has shown he doesn’t have the qualities necessary to be a good commander in chief.”

Admiral McRaven, in an interview on the 76th anniversary of D-Day, noted that those wartime leaders inspired Americans with “their words, their actions and their humanity.”

In contrast, he said, Mr. Trump has failed his leadership test. “As we have struggled with the Covid pandemic and horrible acts of racism and injustice, this president has shown none of those qualities,” Admiral McRaven said. “The country needs to move forward without him at the helm.”

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Credit…Francisco Kjolseth/The Salt Lake Tribune, via Associated Press

Mr. Trump won election in 2016, of course, in spite of a parade of Republicans and retired military officers who refused to support him. Far more current G.O.P. elected officials are publicly backing Mr. Trump than did four years ago. Among his unwavering supporters are Republican leaders like Mitch McConnell, the Senate majority leader, and past foes like Senators Ted Cruz and Lindsey Graham. And polls today indicate that rank-and-file Republicans are squarely behind the president, although that is in part because some Republicans who can’t abide Mr. Trump now align with independents.

Yet it would be a sharp rebuke for former Trump administration officials and well-known Republicans to buck their own standard-bearer. Individually, they may not sway many votes — particularly at a time of deep polarization. But their collective opposition, or even resounding silence, could offer something of a permission structure for Trump-skeptical Republicans to put party loyalty aside.

John Kelly, Mr. Trump’s former chief of staff and a retired Marine general, would not say whom he would vote for, though he did allow that he wished “we had some additional choices.”

Dan Coats, the former Republican senator who was Mr. Trump’s director of national intelligence, “has been concerned about the negative effect on the intelligence community by the turmoil of turnover at D.N.I.,” said Kevin Kellems, a longtime adviser to Mr. Coats, adding that the former spy chief is “encouraged by the confirmation of a new D.N.I. and career intelligence deputy.”

As for whom Mr. Coats will vote for, “ultimately he remains a loyal Republican but he believes the American people will decide on Nov. 3,” said Mr. Kellems.

Joseph Maguire, a retired three-star admiral who served as Mr. Trump’s acting intelligence chief, invoked the comments of Mr. Mattis and two former chairmen of the Joint Chiefs of Staff who also criticized the president this week.

“Jim Mattis, Mike Mullen and Marty Dempsey are all good friends, and I respect them tremendously,” Admiral Maguire said in an interview. “I am in alignment with their views.”

Asked who Mr. Boehner and Mr. Ryan will vote for in November, representatives to both former House speakers declined to say.

Colin Powell and Condoleezza Rice, who both served as secretary of state under George W. Bush, have also so far declined to state their intentions.

A number of current G.O.P. lawmakers and governors are also wrestling with what to do — and what to say — as they balance conscience, ideology and the risk to themselves and their constituents that comes from confronting Mr. Trump.

Representative Francis Rooney of Florida has donated millions of dollars to Republican candidates over the years, served as President Bush’s ambassador to the Vatican and hasn’t voted for a Democrat in decades.

But Mr. Rooney said he is considering supporting Mr. Biden in part because Mr. Trump is “driving us all crazy” and his handling of the virus led to a death toll that “didn’t have to happen.”

Mr. Rooney is not seeking re-election, so is not worried about future electoral prospects. He said his hesitation with Mr. Biden owes to uncertainty about whether left-wing Democrats would pull the former vice president out of the political mainstream.

“What he’s always been is not scary,” said Mr. Rooney. “A lot of people that voted for President Trump did so because they did not like Hillary Clinton. I don’t see that happening with Joe Biden — how can you not like Joe Biden?”

Mr. Rooney has been gently lobbied by one of Mr. Biden’s closest allies in Congress: Senator Chris Coons of Delaware, who has effectively become the former vice president’s emissary to current and recent Republican lawmakers.

Mr. Coons said a number of G.O.P. senators, regardless of their public comments, would ultimately not pull the lever for Mr. Trump in the privacy of the ballot booth.

“I’ve had five conversations with senators who tell me they are really struggling with supporting Trump,” said Mr. Coons, who declined to give names.

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Credit…Al Drago for The New York Times

Indeed, one Republican senator, who is publicly supporting the president, said in an interview that he might prefer a Biden victory if the G.O.P. managed to preserve its Senate majority. This lawmaker, like a number of Republicans, is uneasy with Mr. Trump’s behavior and weary from the near-weekly barrage of questions from reporters about the latest presidential eruption.

As former Senator Claire McCaskill of Missouri, a moderate Democrat who was friends with a number of her former Republican colleagues, put it: “It’s easier to count the ones who are definitely voting for Trump.”

Among the anti-Trump Republicans now out of office, recent events have only vindicated their sense of alarm — and nudged them toward embracing Mr. Biden.

“For people who were long waiting for that pivot, the last week has shown, if anything, he’s dug in and not even making an attempt to appeal to anybody outside his hard base,” said former Senator Jeff Flake of Arizona, who is close to Mr. Coons and in conversation with him about how and when to formalize his support for Mr. Biden.

Former Representative Mark Sanford, who briefly challenged the president in the Republican primary, said last year that he’d support the president if he won the nomination.

But now Mr. Sanford believes Mr. Trump is threatening the stability of the country. “He’s treading on very thin ice,” said Mr. Sanford, also a former South Carolina governor, who is engaged in frequent conversations with other Republicans about how to proceed.

There are already a number of Republican groups dedicated to defeating Mr. Trump, and former lawmakers, strategists and policymakers who are plotting what and when to say about the election.

“There is an organized effort about how to make our voices useful in 2020,” said Kori Schake, who worked at the National Security Council and State Department under President George W. Bush and was an editor with Mr. Mattis of the book “Warriors and Citizens,” about the civil-military divide.

She said a number of officials who worked for both Presidents Bush and Reagan, many of whom signed a 2016 letter opposing Mr. Trump, were on Zoom chats and group emails trying to determine how to express their opposition and whether it should come with an endorsement for Mr. Biden. The effort to gather more anti-Trump Republicans to speak out is being spearheaded by John B. Bellinger III, who also worked in George W. Bush’s N.S.C. and State Department.

Some Republicans believe Mr. Mattis made their task easier.

“It laid the cornerstone of fighting back against Trump,” said former Senator John W. Warner of Virginia, who noted that as Navy secretary he once served as “boss” to Mr. Mattis, then a youthful Marine officer. “He said: ‘I can judge the man.’”

Yet neither Mr. Mattis, nor any other former Trump official, is likely to be able to prod Mr. Bush to publicly state his opposition. Freddy Ford, a spokesman for Mr. Bush, said the former president would stay out of the election and speak only on policy issues, as he did this week in stating that the country must “examine our tragic failures” on race.

Notably, though, while the former president, whom Mr. Trump has never reached out to while in office, may be withdrawn from presidential politics, he is not totally disengaged from campaigns: he has raised money for a handful of Republican senators, including John Cornyn of Texas, Susan Collins of Maine and Cory Gardner of Colorado.

Mr. Romney this week lavished praise on Mr. Mattis but stayed mum about who he would actually support for president.

As for Mrs. McCain, she has sought to stay out of partisan politics. “Picking a fight with Trump is no fun,” said Rick Davis, a longtime McCain adviser who’s close to the family.

But, Mr. Davis, alluding to Mr. Biden, said: “You know where her heart is. Whether she articulates that or not is still an open question.”

Eric Schmitt contributed reporting.