Republicans are bracing for Donald J. Trump to announce an unusually early bid for the White House, a move designed in part to shield the former president from a stream of damaging revelations emerging from investigations into his attempts to cling to power after losing the 2020 election.

While many Republicans would welcome Mr. Trump’s entry into the race, his move would also exacerbate persistent divisions over whether the former president is the party’s best hope to win back the White House. The party is also divided over whether his candidacy would be an unnecessary distraction from midterm elections or even a direct threat to democracy.

Mr. Trump has long hinted at a third consecutive White House bid and has campaigned for much of the past year. He has accelerated his planning in recent weeks just as a pair of investigations have intensified and congressional testimony has revealed new details about Mr. Trump’s indifference to the threat of violence on Jan. 6 and his refusal to act to stop an insurrection.

Mr. Trump has also watched as some of his preferred candidates have lost recent primary elections, raising hopes among his potential Republican competitors that voters may be drifting from a politician long thought to have an iron grip on the party.

Rather than humble Mr. Trump, the developments have emboldened him to try to reassert himself as the head of the party, eclipse damaging headlines and steal attention from potential rivals, including Gov. Ron DeSantis of Florida, a rising favorite of donors and voters. Republicans close to Mr. Trump have said he believes a formal announcement would bolster his claims that the investigations are politically motivated.

Mr. Trump would enter the race as the clear front-runner, with an approval rating among Republicans around 80 percent, but there are signs that a growing number of the party’s voters are exploring other options.

“I don’t think anyone is inevitable,” said Haley Barbour, a former Republican National Committee chairman who also served eight years as Mississippi’s governor.

The timing of a formal announcement from Mr. Trump remains uncertain. But he recently surprised some advisers by saying he might declare his candidacy on social media without warning even his own team, and aides are scrambling to build out basic campaign infrastructure in time for an announcement as early as this month.

That timing would be extraordinary — presidential candidates typically announce their candidacies in the year before the election — and could have immediate implications for Republicans seeking to take control of Congress in November. Mr. Trump’s presence as an active candidate would make it easier for Democrats to turn midterm races into a referendum on the former president, who since losing in 2020 has relentlessly spread lies about the legitimacy of the election. Some Republicans fear that would distract from pocketbook issues that have given their party a strong advantage in congressional races.

“Republicans want to win badly in 2022, and it is dawning on many of them that relitigating the 2020 election with Trump’s daily conspiracy diatribes are sure losers,” said Dick Wadhams, a Republican strategist and former chairman of the Colorado Republican Party.

The former president’s team remains divided over whether he should even run again. Those opposed to a third White House bid have expressed concerns ranging from doubts about Mr. Trump’s remaining political potency to questions about whether he can articulate a clear rationale for running and avoid a repeat of 2020.

Others are urging Mr. Trump to take his time. Donald Trump Jr., his eldest son, has taken a more central role in Mr. Trump’s inner circle of political advisers and has told others that he wants his father to install a more expansive campaign team around him in preparation for a run.

One of the most compelling arguments against an early announcement had been federal campaign finance laws. If and when Mr. Trump announces, he would be ineligible to use any of the $100 million that he has parked in his political action committee to directly support his presidential run. His campaign would also be constrained by a strict $2,900-per-person donation cap for the primaries, meaning he could tap his largest donors only once over the next period of roughly two years to directly fund a candidacy.

But Mr. Trump’s command over small-dollar donors has remained strong, leaving some on his team unconcerned about the fund-raising limits.

The debate over timing comes as investigations into the behavior of Mr. Trump and his associates are gathering steam. The Justice Department is looking into efforts to keep Mr. Trump in office after his defeat. Prosecutors in Fulton County, Ga., have convened a grand jury as part of an investigation into whether the former president and his team tried to influence the vote count there. Each is separate from the House committee scrutinizing his conduct in the run-up to the riot at the Capitol on Jan. 6.

Among those urging Mr. Trump to announce soon is Senator Lindsey Graham of South Carolina. Mr. Graham said the former president would be blamed for — or credited with — whatever happened in the November elections and suggested that an early announcement would focus Mr. Trump’s attention on policy.

“It’s up to him if he runs or not,” Mr. Graham said in an interview. “But the key to him being successful is comparing his policy agenda and policy successes with what is going on today.”

Other Republican leaders have sought to dissuade Mr. Trump from an early announcement.

Ronna McDaniel, the chairwoman of the Republican National Committee, had urged Mr. Trump to wait until after the midterms, worried that news about his campaign could derail the party’s midterm messaging. One R.N.C. official noted that when Mr. Trump opened a campaign, the party would stop paying his legal bills related to an investigation by the New York attorney general. Still, Ms. McDaniel has recently resigned herself to the idea that he will announce before the elections, according to people familiar with the conversations.

But even Trump aides who are supportive of another campaign worry that the former president’s path to a third nomination has become more difficult than he’s willing to acknowledge.

Some close to Mr. Trump have grown concerned about potential legal and political consequences from the congressional hearings into the Capitol riot. Cassidy Hutchinson, a former White House aide, testified this week that Mr. Trump had known that some of his supporters were carrying weapons that day and had still encouraged his team to let them through security checkpoints. Representative Liz Cheney, a Wyoming Republican who is on the committee, said the panel had evidence of witness tampering.

Mr. Trump signaled his concern about the potential political consequences of the testimony, reacting in real time to the hearing by posting a dozen messages on his Truth Social website attacking Ms. Hutchinson and denying her most explosive testimony.

Few Republican officeholders have spoken publicly about the hearings, and most have either said nothing about the congressional investigation or dismissed it as a partisan sham. But there have been signs that Republicans recognize its potential power.

“Ms. Hutchinson would be the star member of a women’s Republican club — a committed conservative, no reason to say anything but the truth,” said Senator Bill Cassidy of Louisiana, who voted to convict in Mr. Trump’s second impeachment and has been a target of Mr. Trump’s since. He was one of the few lawmakers who spoke on the record. “It gives power to a testimony that allows Americans to judge for themselves.”

Mick Mulvaney, one of Mr. Trump’s four White House chiefs of staff, told CBS News he could no longer defend Mr. Trump after hearing Ms. Hutchison’s claims. In an interview afterward, he said he heard from two dozen political appointees from the Trump administration who had thanked him for his comments and told him they agreed.

Mr. Mulvaney declined to say whether he would vote for Mr. Trump if he was the nominee in 2024. Nonetheless, people close to Mr. Trump took note of the televised statements and made calls this week looking for someone who could attack and therefore undermine Mr. Mulvaney in South Carolina, the former adviser’s home state, said one political operative with knowledge of the calls.

The past two months of weekly primary contests have proved that Mr. Trump’s policies have reshaped the Republican Party. But the red-capped constituency has also repeatedly demonstrated its independence from the patriarch of the Make America Great Again movement. While Republican primary voters backed some of Mr. Trump’s favored candidates, particularly in Senate primaries, they rejected his picks in Georgia, Idaho, Nebraska and elsewhere.

“There’s some evidence that some Republican voters are trying to slow-walk from Donald Trump,” said Scott Jennings, a Republican strategist. Jennings said he was not surprised by Mr. Trump’s eagerness to jump into the presidential race. “If you’re in his shoes, you have to try to put that fire out. Because the more it burns, the more it burns.”

In interviews with two dozen Republican voters, party activists and elected officials, few said the Jan. 6 hearings were playing a role in their interest in other candidates. But several noted that they were looking for a nominee who was less divisive.

​​“There will be a number of Republicans who many Republicans feel cannot only unite the party but would govern with strong, conservative policies,” said Jason Shepherd, a former Newt Gingrich aide who is a Georgia Republican Party state committeeman. If Mr. Trump wins the nomination, Mr. Shepherd said, Republicans will not hesitate to back him in the general election.

Nicole Wolter, the chief executive of a suburban Chicago manufacturing firm and a member of the board of the National Association of Manufacturers, has an office decorated with photos of her visiting the White House during Mr. Trump’s years as president.

But, Ms. Wolter said in an interview last month in her office in Wauconda, Ill., Mr. Trump has become too toxic to the voters in suburbs for Republicans to win the general election.

“There’s just too many people who don’t really like him,” Ms. Wolter said. “We want everyone to kind of rally around him and be able to get the independents, and I just think that if he ran, he wouldn’t be able to pull that off.”

Post-presidency polls have consistently shown that Mr. Trump remains the most powerful figure inside his party. But potential competitors have not been scared off.

Last week, a survey of Republicans in New Hampshire, an early presidential primary state, showed a statistical tie between Mr. Trump and Mr. DeSantis.

Former Secretary of State Mike Pompeo, who told Mr. Trump last year that he wouldn’t compete against him for the presidential nomination, has continued to lay the groundwork for a 2024 bid.

Mr. Pompeo has told others that he can beat Mr. Trump in the Iowa caucuses, according to people familiar with the conversations.

Jonathan Martin and Shane Goldmacher reporting.