WASHINGTON — Representative Kevin McCarthy of California, the minority leader, on Monday scrounged for the support he would need to become speaker of the House if Republicans gain control of the chamber, facing resistance from a newly emboldened right flank as Republicans grappled with their historically weak performance in the midterm elections.
With the Senate in Democratic hands and control of the House still up in the air, Republicans began the week — which they had expected would be a triumphant victory lap — limping toward the finish and bitterly divided over who should lead what was shaping up to be a tiny and unruly majority.
“No one in this town has 218 votes for speaker of the House, so we’re going to have a debate and make sure that we set up the structure properly to then figure out how someone will get 218 votes,” Representative Chip Roy, Republican of Texas and a member of the ultraconservative Freedom Caucus, said as he emerged from a nearly hourlong meeting in Mr. McCarthy’s Capitol office suite.
The Freedom Caucus has threatened to run a protest candidate against Mr. McCarthy, although no challenger has emerged, and has insisted that he overhaul party rules to weaken the speaker’s power and give more sway to the rank-and-file. That could make his life exceedingly difficult if he manages to secure the top job, effectively allowing any Republican to move to dump him at any moment and complicating the task of moving virtually any major legislation through the chamber.
The meeting came one day before Mr. McCarthy was to face his first test in his quest to lead the House. Republicans were scheduled to hold internal leadership elections on Tuesday. The vote will be a major barometer for Mr. McCarthy’s standing, though he will still need to win the speakership at the start of the new Congress in an election on the floor in which all members have a vote.
On Monday, some right-wing Republicans made it clear he had yet to win them over.
“I am willing to support anybody that’s willing to change dramatically how things are done here so that members are empowered, fairly and equitably,” said Representative Scott Perry of Pennsylvania, the chairman of the Freedom Caucus. He declined to say whether he would back Mr. McCarthy or another candidate but said the group’s members had a “cordial” and “productive” talk with Mr. McCarthy.
At the same time, in a further indication of divisions within the party about what should come next, leaders of some of the most powerful hard-right organizations in Washington sent a letter on Monday calling on House and Senate Republicans to delay their leadership elections scheduled for this week.
“The Republican Party needs leaders who will confidently and skillfully present a persuasive coherent vision of who we are, what we stand for and what we will do,” wrote the signers, including leaders from the Club for Growth, the Heritage Foundation and the Conservative Partnership Institute. “Many current elections are still undecided. There should be no rushed leadership elections.”
There was no indication the prodding would have any effect in the Senate, where party leaders have shrugged off calls to delay their leadership elections scheduled for Wednesday. And as of Monday, no opponent to Senator Mitch McConnell of Kentucky, the minority leader, had emerged, and he was expected to retain his position.
The calculus for Mr. McCarthy was more complex. A poor showing on Tuesday in his conference’s internal elections would embolden lawmakers in the party’s right flank, many of whom have sought for years to weaken Mr. McCarthy.
The landscape was also complicated by former President Donald J. Trump looming in the wings. Mr. Trump, who received an unusual torrent of internal blame after a string of midterm losses by candidates he had handpicked, was expected to announce that he would run for president again just hours after Mr. McCarthy was to face his conference in an election that would include newly elected Republicans as well as candidates in races yet to be called.
“Members have a lot of questions,” said Representative Byron Donalds, who is running for the No. 4 leadership position. “Number one, obviously the expectations were not delivered. Number two, how are we actually going to govern what’s going to be a small majority?”
Mr. Donalds continued: “We have to actually lay out a demonstrated plan; serious policies that voters actually believe in and we can’t equivocate from that, even in what’s looking to be continued gridlock government. Republican members want to get answers to that, and I think that’s going to be critical toward Kevin’s ability to becoming the leader, and eventually the speaker.”
Mr. McCarthy received support on Monday from Representative Marjorie Taylor Greene, Republican of Georgia, one of the party’s most prominent far-right lawmakers who is close to Mr. Trump.
In an interview with Steve Bannon, a former Trump adviser, on his podcast, Ms. Greene called attempts to challenge Mr. McCarthy for speaker “risky” and a “bad strategy,” arguing that it could empower Democrats.
“Here’s the harsh reality,” Ms. Greene said. “There are Republicans in our conference that would make a deal with the Democrats and cross over.”