Republican leaders scrambled on Wednesday to tamp down support in their ranks for bipartisan legislation creating an independent commission to investigate the Jan. 6 Capitol assault, as the House moved toward an evening vote.

Party leaders, led by Representative Kevin McCarthy of California, formally announced their opposition on Tuesday, arguing that their members should not support any accounting of the deadly pro-Trump mob that attacked Congress without also studying “political violence” on the left. Then, after initially pledging neutrality, they also began lobbying lawmakers to vote no.

Former President Donald J. Trump sought to add his own pressure, chastising Republicans to “get much tougher” and oppose the inquiry unless it was expanded to look at “murders, riots and fire bombings” in cities run by Democrats.

“Hopefully, Mitch McConnell and Kevin McCarthy are listening!” he said.

But as the vote neared, top Republicans were facing the possibility of a wave of defections that threatened to once again drive a wedge through a party struggling to unite in the wake of Mr. Trump’s mendacious campaign to overturn the 2020 election. A significant splintering would be particularly embarrassing for Mr. McCarthy, who after ousting his No. 3 last week for her views on Mr. Trump, vowed to unite the party around the former president ahead of the 2022 midterms.

The bipartisan House Problem Solvers Caucus, which includes 29 Republicans, formally endorsed the commission late Tuesday. Other Republicans privately said they were inclined to vote “yes” in a show of solidarity with Representative John Katko, Republican of New York, who negotiated the terms of the commission at Mr. McCarthy’s behest, only to have the leader turn around and trash the product.

Mr. Katko argued on Tuesday that the commission offered Congress the best chance to dispense with politics and really get to the bottom of an attack that most members of Congress witnessed themselves in horrid detail and both parties deemed a disastrous security failure.

“We both dispensed with our politics to do what the greater good is,” he said.

Modeled after the commission that studied the Sept. 11, 2001, terrorist attacks, the 10-person panel would be tasked with exhaustively studying the causes of the attack and the intelligence and security lapses that allowed thousands of pro-Trump supporters, some of them armed, to overwhelm police and overtake the Capitol, sending the then-vice president and Congress into hiding. Its work would be fast: The legislation calls for the body to produce a report, including recommendations to prevent future violence, by Dec. 31.

House Democrats are expected to unanimously back the commission, and President Biden formally endorsed it on Tuesday.

Furious over Mr. McCarthy’s furious work to undermine it, especially after they agreed to several of his key demands in negotiations, Democrats trained their fire on the leader ahead of the vote. Democratic lawmakers, and even some Republicans, speculated that Mr. McCarthy’s opposition could be driven in part by an effort to prevent damaging information about his own conversations with Mr. Trump around Jan. 6 from coming to light at a time when he is trying to help his party retake the House and become speaker.

“My humble opinion is that there’s some information that he would deem troubling for the Republican Party if it got out, and I think he will do everything possible to prevent that,” said Representative Bennie Thompson, Democrat of Mississippi, who co-wrote the commission bill with Mr. Katko.

The commission’s fate, though, will almost certainly be decided in the Senate, where Democrats would need at least 10 Republicans to agree to support its formation.

Senator Mitch McConnell of Kentucky, the minority leader, told reporters that he and other Republican senators were undecided and would “listen to the arguments on whether such a commission is needed.” During a private lunch with his members on Tuesday, Mr. McConnell stressed that if Senate Republicans banded together, they could most likely force changes to its structure, including changes to make the hiring of staff more bipartisan.