CNN  — 

House GOP Leader Kevin McCarthy still does not have enough vote commitments to be the next speaker following a nearly hour-long call with various factions of the Republican conference, and even as he has made a number of significant concessions in recent days.

McCarthy is racing the clock to try to lock down votes ahead of the House vote to elect a new speaker on Tuesday.

The call, which was described by multiple sources as collegial, focused on some of the same sticking points that have languished for weeks within GOP ranks. Republicans committed to continue working throughout the weekend to find a resolution, with lawmakers acknowledging there are still major issues to work through.

“Rules are still in discussion. No concrete package to show at moment,” one GOP lawmaker told CNN. “But if support is there, we may have some agreements.”

House Republicans have been debating whether to reinstate an arcane rule that would empower any member to bring up a vote to oust a sitting speaker at any time. For McCarthy’s backers, the so-called motion to vacate the speaker’s chair is seen as something that could be used by the right flank to hamstring his ability to lead the conference and effectively govern.

In one separate breakthrough, however, McCarthy did say he was open to moving forward with a committee that would investigate federal government activity and look into political partisanship at agencies, such as the FBI and the Justice Department.

What form that committee takes is still unclear, but it has been a top ask from conservatives such as Rep. Chip Roy of Texas. This would centralize the myriad probes into the Biden administration into a single panel, but the idea could run into resistance from the soon-to-be committee chairs, who have already begun work on the House GOP’s planned investigations.

Another concern is over whether the various concessions will even deliver enough votes to make McCarthy the speaker. In a positive sign for McCarthy, another GOP lawmaker did say that some Republicans, who previously considered themselves on the fence, announced on Friday’s call that they are now leaning toward McCarthy based on the ongoing negotiations.

One previously undecided lawmaker, Rep. Morgan Griffith of Virginia, announced in a statement Friday evening that he would support McCarthy.

Griffith, a senior member of the hardline House Freedom Caucus who was on the Friday call, said McCarthy has agreed to “a rule that legislation will only have a single purpose” as well as another change that would require “a stricter germaneness rule.”

“A single bill should not be a hodgepodge of issues totaling thousands of pages,” Griffith said in the statement. “I believe these changes can dramatically improve our legislative process. Because Leader McCarthy agreed to these rules changes, I have agreed to vote for him for Speaker of the House.”

On the motion to vacate, McCarthy has expressed an openness to lowering the threshold down to five members, which is something members of the Freedom Caucus are pushing for. But one source told CNN that there was “deep hesitancy” from other members who fear that lowering the threshold could hold the conference hostage in the months to come.

The source told CNN there was “a lot of frustration over opening this back up.”

Some House Republicans have pressed for a process that would allow any single member to hold a floor vote on ousting the sitting speaker, which was wielded over former Speaker John Boehner before he was forced out of the job by the far right in 2015.

McCarthy has been adamantly opposed to restoring the “motion to vacate the chair,” and a majority of the House GOP voted against the idea during a closed-door meeting in November.

Source: www.cnn.com