Senator Mitch McConnell of Kentucky, the majority leader, and his deputies have made clear to colleagues that they strongly oppose the effort to reverse the election results, but Mr. Hawley has said he will force a vote and at least 12 other Republican senators plan to back him. The party fissures have extended to the House, where the top Republican, Representative Kevin McCarthy of California, has not revealed how he plans to vote on Jan. 6 but has said he is supportive of those who want to have a debate, while Representative Liz Cheney of Wyoming, the No. 3 Republican, has argued vociferously against the move.
That has created something of a free-for-all in the House. Lawmakers have been left to weigh on their own whether to vote to protect the sanctity of the election and risk incurring the wrath of their constituents, or move to overturn the results in a doomed loyalty test that could badly damage their party.
Representative Thomas Massie, Republican of Kentucky, said in an interview that he and the other conservatives who came out on Monday against the challenge were hoping to put forward a “constitutionally grounded” argument from a “pro-Trump perspective” that their colleagues could adopt.
“I think there are a lot of people of the same mind as us, but they were looking for some kind of grounding or maybe some kind of cover,” Mr. Massie said. “I feel like there are people getting sucked into the other vortex as the hours go by.”
Other Republicans, including some of the president’s most ardent defenders, were plainly uneasy about the coming vote, prompting a series of tortured statements seeking to justify the most basic of democratic positions: a vote to respect the outcome of an election.
“The easiest vote for me politically would be to object to everything and vote for every objection,” Senator Kevin Cramer, Republican of North Dakota, said on Sunday. On Monday, Mr. Cramer issued a statement saying he would not object, adding “objecting to the Electoral College votes is not an appropriate or effective way to change the results.”
Senator Rob Portman, an Ohio Republican who is up for re-election in 2022, said in a lengthy statement that he voted for Mr. Trump but could not object to certifying the election results, citing his opposition to a similar, Democratic-led effort in 2005.