(CNN) House Republican Leader Kevin McCarthy has offered a key concession to critics of his bid for the House speakership during private conversations this week: reducing the threshold that is required to force a floor vote on ousting the sitting speaker, according to six Republican sources familiar with the internal discussions.
McCarthy has been trying to find a compromise threshold that would appease his critics enough to earn their speaker vote, while still being palatable to the rest of the House GOP, and has been sounding out all corners of the conference in private phone calls this week.
One of the numbers that has come up in recent conversations between McCarthy and GOP lawmakers -- and which has not been previously reported -- is a five-person threshold, according to two of the Republican sources.
Currently, the majority of the House GOP is required to call for the so-called motion to vacate the speaker's chair. But some conservative hardliners are pushing for a single member to be able to call for such a vote, which they see as an important mechanism to hold the speaker accountable.
A five-person threshold, however, may be too low for the moderate wing of the party, some of whom have privately suggested they would be willing to agree on a 50-person threshold.
And some of McCarthy's fiercest critics, including Reps. Matt Gaetz of Florida and Ralph Norman of South Carolina, told CNN they see the five-person threshold as still too high, underscoring the significant challenge McCarthy faces as he works to lock down the speakership.
"No, less than 5!!" Norman said in a text message of the proposed motion to vacate threshold. "2 or less (my opinion)."
And Gaetz said: "He's gotta get down to 1."
All of this will be a major topic of discussion during a crucial conference call on Friday afternoon that McCarthy scheduled with the various ideological caucuses in the House GOP, just four days ahead of the January 3 speaker's vote.
A compromise on the motion to vacate -- which McCarthy previously said he would not budge on -- could be key to unlocking the votes he needs to secure the speakership. And his willingness to negotiate on the issue also shows how desperate McCarthy is to seal the deal, even if it means giving away some of his power.
Still, other challenges remain. McCarthy, for example, wants a commitment from the holdouts that they will vote for him for speaker if he agrees to come down on the motion to vacate, but his critics want to see him make an ironclad commitment before they lend him their support.
"The 'devil is in the details' as far as threshold & other rule concessions," Norman said. "Until the details are spelled out, in writing and sealed with social media posts, people will not move on votes."