WASHINGTON — The new Congress opens with House Republican leader Kevin McCarthy grasping for his political survival, with the potential to become the first nominee for speaker in 100 years to fail to win initial support from his own colleagues in a high-stakes vote for the gavel.

Lawmakers convene Tuesday to a new era of divided government as Democrats relinquish control of the House after midterm election losses. While the Senate remains in Democratic hands, barely, House Republicans are eager to confront President Biden’s agenda after two years of a Democratic Party monopoly on power in Washington.

But first, House Republicans must elect a speaker.

Mr. McCarthy is in line to replace Speaker Pelosi, but he heads into the vote with no guarantee of success. The California Republican faces entrenched detractors within his own ranks. Despite attempts to cajole, harangue and win them over — even with an endorsement from President Trump — Mr. McCarthy has fallen short.

The noontime showdown could very well devolve into a prolonged House floor fight, a spectacle that divides the Republican Party, weakens its leadership and consumes the first days of the new Congress.

“This is a lot more important than about one person,” said a former Republican leadership senior aide, Doug Heye. “It’s about whether Republicans will be able to govern.”

House Republicans will huddle behind closed doors early in the morning, ahead of the floor action, as newly elected lawmakers arrive for what’s traditionally a celebratory day. Families in tow, the members of the new Congress prepare to be sworn into the House and Senate for the start of the two-year legislative session.

A new generation of Trump-aligned Republicans are leading the opposition to Mr. McCarthy, inspired by the former president’s Make America Great Again slogan. They don’t think Mr. McCarthy is conservative enough or tough enough to battle Democrats. 

It’s reminiscent of the last time Republicans took back the House majority, after the 2010 midterms, when the tea-party class ushered in a new era of hardball politics, eventually sending Speaker Boehner to an early retirement.

Typically it takes a majority of the House’s 435 members, 218 votes, to become the speaker. With just a slim 222-seat majority, Mr. McCarthy can afford only a handful of detractors. A speaker can win with fewer than 218 votes, as Mrs. Pelosi and Mr. Boehner did, if some lawmakers are absent or simply vote present.

But Mr. McCarthy has failed to win over a core — and potentially growing — group of right-flank Republicans led by the conservative Freedom Caucus, despite weeks of closed-door meetings and promised changes to the House rules. Nearly a dozen Republicans have publicly raised concerns about Mr. McCarthy.

“Kevin McCarthy doesn’t have to 218 votes to be speaker,” Representative Scott Perry of Pennsylvania, the chairman of the Freedom Caucus and a leader in Mr. Trump’s efforts to challenge the 2020 election, said in an interview with the Associated Press. “Unless something dramatically changes, that’s where we’re going to be.”

Late Monday evening, Mr. McCarthy met with Mr. Perry in the speaker’s office at the Capitol, a Republican aide confirmed on condition of anonymity to discuss the private session.

Yet the prospect of holdouts causing havoc on Day One has launched a counter-offensive from Republicans who are frustrated that the detractors threaten the workings of the new Congress.

A sizable but less vocal group of Mr. McCarthy supporters started its own campaign, “Only Kevin,” as a way to shut down the opposition and pledge their support only to him.

A viable challenger to McCarthy had yet to emerge. Representative Andy Biggs of Arizona, a former leader of the Freedom Caucus, was running against Mr. McCarthy as a conservative option, but was not expected to pull a majority. Mr. McCarthy defeated him in the November nominating contest, 188-31.

The second-ranking House Republican, Representative Steve Scalise of Louisiana, would be an obvious next choice, a conservative widely liked by his colleagues and seen by some as a hero after surviving a brutal mass shooting during a congressional baseball game practice in 2017.

Once rivals, Messrs. McCarthy and Scalise have become a team. Mr. Scalise’s office rejected as “false” a suggestion Monday by another Republican that Mr. Scalise was making calls about the speaker’s race.

Mr. McCarthy vowed to fight to the finish, going multiple rounds of painstaking floor votes — a sight unseen in Congress since the disputed speaker’s race of 1923.

“It would be nice if we can be ready to go on January 3,” said Representative Jim Jordan of Ohio, who is set to become chairman of the House Judiciary Committee. “But you know, if it doesn’t happen on the first ballot, that’s when that just pushes things back.”

Without a speaker, the House cannot fully form — naming its committee chairmen, engaging in floor proceedings and launching the investigations of the Biden administration that are expected to be core to the Republicans’ agenda.

The upheaval in the House on the first day of the new session could be in stark contrast to the other side of the Capitol, where the Senate Republican leader, Mitch McConnell, will officially become the chamber’s longest-serving party leader in history.

Despite being in the minority in the Senate, where Democrats hold a slim 51-49 majority, Mr. McConnell could prove to be a viable partner as Mr. Biden seeks bipartisan victories in the new era of divided government. 

The two men were expected to appear together later in the week in the GOP leader’s home state of Kentucky to celebrate federal infrastructure investment in a vital bridge that connects Kentucky and Ohio.

Mr. McCarthy’s candidacy for speaker should have been an almost sure thing. Affable and approachable, he led his party into the majority, having raised millions of campaign dollars and traveled the country to recruit many of the newer lawmakers to run for office.

Yet Mr. McCarthy has been here before, abruptly dropping out of the speaker’s race in 2015 when it was clear he did not have support from conservatives to replace Mr. Boehner.

One core demand from the holdouts this time is that Mr. McCarthy reinstate a rule that allows any single lawmaker to make a “motion to vacate the chair” — in short, to call a vote to remove the speaker from office.

Ms. Pelosi eliminated the rule after conservatives used it to threaten Mr. Boehner’s ouster, but Mr. McCarthy agreed to add it back in — but at a higher threshold, requiring at least five lawmakers to sign on to the motion.

“I will work with everyone in our party to build conservative consensus,” Mr. McCarthy wrote in a weekend letter to colleagues.

As Mr. McCarthy convened a New Year’s Day conference call with Republican lawmakers to unveil the new House rules package, Mr. Perry dashed off a fresh letter of concerns signed by eight other Republicans saying that the changes do not go far enough.

Associated Press