Vote for Trump? These Republican Leaders Aren’t on the Bandwagon.

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 Trump has never reached out to while in office, may be withdrawn from presidential politics, he is not totally disengaged from campaigns: he has raised money for a handful of Republican senators, including John Cornyn of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.