Originally Published: 03 JAN 23 05:00 ET

Updated: 03 JAN 23 11:42 ET

By Clare Foran, Melanie Zanona, Annie Grayer and Kristin Wilson, CNN

(CNN) -- House GOP leader Kevin McCarthy faces a make-or-break moment on Tuesday, as he seeks to lock down the support necessary to become the next speaker in a vote that could turn into a chaotic and contentious once-in-a-century floor fight.

The 118th Congress is set to convene to elect a new speaker, but McCarthy does not yet have the votes to secure the gavel -- a major problem for the California Republican that threatens to tear apart the incoming House GOP majority. If McCarthy fails to shore up the support he needs to win in the initial round of voting, the race for speaker could go to multiple ballots -- something that hasn't happened since 1923.

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McCarthy faces a small but determined contingent of hardline conservatives. The group is using the leverage they have in the razor-thin Republican majority to extract concessions as they threaten to deny the GOP leader critical votes. McCarthy has already given in to a number of their demands, including making it easier to topple the sitting speaker, but it is unclear whether his efforts will be enough.

A closed-door meeting of House Republicans on Capitol Hill grew tense and heated Tuesday morning as uncertainty mounts over McCarthy's fate.

McCarthy raised his voice and was animated as he teed off against his opponents and detailed concessions he has made, according to two sources. "I've earned this job," he said.

GOP Rep. Mike Rogers, a McCarthy ally and the incoming chair of the House Armed Services Committee said in the closed-door meeting with the GOP conference that anyone who votes against McCarthy doesn't get on a committee, according to two sources. CNN previously reported this was a threat McCarthy allies were considering.

McCarthy has made clear he has no plans to drop out of the race even if it goes to multiple ballots on the floor, but the fight has cast a long shadow over the incoming House Republican majority. And the deal-making McCarthy has engaged in to try to win over critics may mean he has a weaker hand to play in his position of authority if he does become speaker.

Sources with knowledge of McCarthy's thinking say he is still confident that he will get the 218 votes to be elected. But there is no way of guessing how long the voting will go or how many ballots it will take.

Uncertain vote math and deal making

To be elected speaker, a candidate needs to win a majority of members who vote for a specific person on the House floor. That amounts to 218 votes if no member skips the vote or votes "present."

House Republicans will hold 222 seats in the new Congress -- so for McCarthy to reach 218 votes, he would only be able to afford to lose four GOP votes. So far, at least five Republicans have vowed to oppose him, with nearly a dozen other GOP lawmakers publicly saying they're still not there yet.

The potential for the election to advance to multiple ballots has raised the question of whether a viable alternative could emerge if McCarthy can't get the votes. The GOP leader's allies and foes alike have attempted to quietly game out what could happen if he fails to secure the gavel on the first round and lawmakers move into uncharted territory.

McCarthy is facing a longshot challenge in the race from hard-right Republican Rep. Andy Biggs. McCarthy has defeated the Arizona congressman before -- by a resounding vote of 188 to 31 in November when the House Republican conference voted for McCarthy to be its leader. But the longshot challenge has still complicated McCarthy's effort to become speaker and threatens to draw support away from the GOP leader in the critical vote.

After the far-right House Freedom Caucus denied his ascension to the speakership in 2015, McCarthy spent years courting the conservative wing of his party and worked hard to stay in former President Donald Trump's good graces.

McCarthy has gotten some key backup from Trump, who publicly endorsed his speaker bid and encouraged others to support McCarthy. His congressional allies have also banded together in effort to act as a counterweight to his critics.

But when a red wave never materialized in the November midterms, the razor-thin majority that resulted for Republicans empowered a small band of conservatives -- long distrustful of McCarthy -- to make demands.

What has unfolded over the last two months is an all-out scramble for the speakership, which has taken the form of strategy sessions with close allies on and off Capitol Hill, intense negotiations over rules changes and non-stop phone calls with members.

McCarthy has been in deal-making mode, but if he does win the gavel, some of the concessions he has made may make it more difficult for him to stave off future challenge to his speakership.

In one change that could weaken his hand in the future, McCarthy has told lawmakers -- as first reported by CNN -- that he would support a threshold as low as five Republicans to trigger a vote on deposing the speaker, known as the "motion to vacate" the speaker's chair, a major concession for him and one that moderates worry will be used as a constant cudgel over his head.

This story has been updated with additional developments Tuesday.