CNN  — 

House GOP Leader Kevin McCarthy is moving swiftly to lock down the votes to claim the speaker’s gavel as a hard-right faction of his conference discusses whether to mount a long-shot challenge to complicate his bid and force concessions in the process, according to multiple GOP sources.

McCarthy privately spoke to his closest advisers and confidantes in a Wednesday morning phone call just hours after his party appeared on track to take the House but fell short of their bullish expectations of a massive GOP landslide. The California Republican tapped a group of members to be on his whip team that will help him secure the 218 votes in order to win the speakership in January, with GOP lawmakers on the call promising to “work hard to get him elected,” according to a source familiar with the matter. And several allies were seen popping in and out of McCarthy’s office on Wednesday as they started to hash out and execute their game plan.

“Yes,” McCarthy said confidently Wednesday night as he left the Capitol and was asked if he had the votes to assume the speakership.

But McCarthy’s easy ascension to the speakership will be determined in large part by the size of a potential GOP majority. If McCarthy maintains a narrow majority, then the pro-Trump House Freedom Caucus could stand in the way of his leadership ambitions. CNN has not yet projected a Republican takeover of the chamber.

A source familiar with the House Freedom Caucus’ deliberations told CNN on Wednesday morning that there are around two dozen current and incoming members who are willing to vote against McCarthy if he doesn’t offer them concessions. They are actively discussing putting up a nominal challenger to face McCarthy in next week’s leadership elections in an effort to force the GOP leader to give them more influence in how the House operates, the source said.

McCarthy, who sent a letter to the conference Wednesday afternoon officially declaring his bid for the speakership and asking members for their support, spoke with some potential GOP holdouts behind closed doors throughout the day, including Georgia Rep. Marjorie Taylor Greene, the controversial conservative who was booted from her committee assignments by Democrats – and a number of Republicans – over her past incendiary rhetoric. Greene has pushed for a spot on the powerful House Oversight Committee in a GOP majority.

Leaving McCarthy’s office, Greene would not say if she’d get what she’s been seeking.

“No comment,” Greene said when asked if she’d support McCarthy for speaker.

Next week’s leadership election is just the first step in the process. McCarthy would need to win a majority of his conference’s support next week to be nominated for speaker before a January vote when he would need 218 votes of the full House to win the gavel. The hope, the source said, is that if they back a challenger to McCarthy in next week’s elections, it would force the California Republican to cut a deal in order to secure their support in the January speaker’s race when he wouldn’t be able to afford to lose more than a handful of GOP votes in a narrow Republican majority.

The Freedom Caucus’ strategy will come into sharper focus by week’s end as members weigh their options and as incoming lawmakers come to Washington for initial meetings. Rep. Matt Gaetz, an unabashed McCarthy critic who is not a member of the Freedom Caucus but is closely aligned with the group, also started calling members to talk strategy about the speaker’s race, according to a source familiar.

Among their demands: Making it easier for individual members to call for a vote ousting a sitting speaker, an idea that McCarthy has long rejected and one that was wielded over former Speaker John Boehner, a Republican from Ohio. The same source said that the Freedom Caucus wants more representation on the panel that makes selections on members’ committee assignments. They are also calling on GOP leaders to commit to slowing down the legislative process and give them more time to review even non-controversial bills.

Hardliners may also push for promises related to launching investigations and impeachment proceedings into President Joe Biden or members of his Cabinet.

Rep. Andy Biggs, an Arizona Republican and former chairman of the Freedom Caucus, told a right-wing streaming network that a McCarthy speakership should not be a “foregone conclusion,” complaining that a red wave never materialized and accusing McCarthy of “backpedaling” on impeachment.

“McCarthy has a lot of chips to cash in,” said a senior GOP source. “But he’s gonna have to cash in every single one of them.”

McCarthy could also win over detectors with plum committee assignments, lush office space and other perks. Prior to Tuesday, there was also talk of adding an extra leadership position to his team, which could also be used to woo critics.

McCarthy allies are touting his Tuesday endorsement from former President Donald Trump for the speaker’s gavel, something that could help with staunch Trump backers in the House GOP conference. Moreover, McCarthy has long moved to develop a good standing with even the most rebellious forces within the Freedom Caucus and has been in talks with some members of the group about their role in a GOP majority for weeks, according to Republican sources.

Plus, McCarthy allies believe Republicans will credit him for the hundreds of millions of dollars that his outside group raised and spent in key races. McCarthy has been calling victorious GOP candidates and members since Tuesday night.

McCarthy’s pitch to members, according to a source familiar, has been relatively straight forward: the GOP picked up seats two cycles in a row under his watch, and he is on the verge of delivering Republicans the majority – which will arm them subpoena power and allow them to serve as a check on the Biden administration.

While McCarthy’s allies say the GOP leader is willing to hear members out, they believe negotiating with members could become a slippery slope – though McCarthy may have no choice, depending on the margins.

McCarthy had hoped to pick up at least 20 seats to give him a cushion in both the speaker’s race and to help push through his agenda. It’s unclear if they can get there as many races remain too early for CNN to call.

Other leadership races in flux

Aside from the speaker’s race, Tuesday’s underwhelming performance for the GOP has scrambled other leadership races.

The race for House GOP whip – a position that will only open up if Republicans win the majority – was already competitive, though Rep. Tom Emmer, who chairs the House GOP’s campaign arm, was seen as having the edge since he was likely to be rewarded if they had a strong night.

Now, Republicans say it could be tougher for Emmer to pull out a win.

Emmer told reporters Tuesday he still plans to run and that he doesn’t know if a smaller majority impacts his bid. But his pitch to members is similar to McCarthy’s, saying: “we delivered.”

Meanwhile, Rep. Jim Banks of Indiana, a Trump ally and the head of the conservative Republican Study Committee, also officially declared his candidacy for the whip’s position. And Rep. Drew Ferguson of Georgia, the current deputy whip, is also vying for the post, arguing that his experience on the whip’s team will be even more valuable in a slimmer majority, where the chief vote counting job will be crucial for governing.

This story has been updated with additional developments.

CNN’s Kristin Wilson and Morgan Rimmer contributed to this report.