CNN  — 

House GOP leader Kevin McCarthy outlined some of the concessions that he has agreed to in his campaign for speaker on a Sunday evening conference call – including making it easier to topple the speaker, according to multiple GOP sources on the call. But McCarthy could not say whether he would have the votes for the speakership, even after giving in to some of the right’s most hardline demands.

Later Sunday evening, House Republicans unveiled their rules package for the 118th Congress, which formalizes some of the concessions that McCarthy has agreed to. The House adopts its rules package only after it selects a speaker, which McCarthy has not locked down, so there could be additional compromises made in the coming days.

In a “Dear Colleague” letter from the California Republican, he made his case for the speakership and offered additional promises, including ensuring that the ideological groups are better represented on committees.

Not long after Sunday’s call, a group of nine hardliners – who had outlined their demands to McCarthy last month – put out a new letter saying some of the concessions he announced are insufficient and making clear they’re still not sold on him, though they did say progress is being made.

“Thus far, there continue to be missing specific commitments with respect to virtually every component of our entreaties, and thus, no means to measure whether promises are kept or broken,” the members wrote in the letter obtained by CNN.

This group is still pushing to give a single lawmaker the power to call for a vote toppling the speaker, and they also want a commitment that leadership won’t play in primaries, among other things. Since McCarthy can only afford to lose four votes on the House floor, it means he still has a lot of work to do before Tuesday.

The California Republican had told his members in Sunday’s call that after weeks of negotiations, he has agreed to a threshold as low as five people to trigger a vote on ousting the speaker at any given time, known as the “motion to vacate” the speaker’s chair, and pitched it as a “compromise.” CNN first reported last week that he was supportive of that threshold.

Some moderates – who fear the motion to vacate will be used as constant cudgel over McCarthy’s head – pushed back and expressed their frustration during the call, sources said.

Rep. Dusty Johnson of South Dakota said he wasn’t happy with the low threshold McCarthy agreed to, though he indicated he would swallow it, but only if it helps McCarthy win the speakership. Other members made clear that the rules package that was negotiated will be off the table if McCarthy’s critics end up tanking his speakership bid.

Rep. Mario Diaz-Balart of Florida pressed McCarthy on whether this concession on the motion to vacate will win him the 218 votes. But he did not directly answer, though McCarthy said earlier on the call that people were “slowly” moving in the right direction.

However, later in the call, Florida Rep. Matt Gaetz – one of the five “hard no” votes for McCarthy – said they would not back McCarthy, despite all the concessions.

Rep. Carlos Gimenez of Florida then repeated Diaz-Balart’s question, asking McCarthy to answer it. McCarthy’s response, according to sources, was that they have a couple days to close the deal, and they need to close.

Rep.-elect Mike Lawler of New York asked Gaetz if he would back McCarthy if he agreed to bring the motion to vacate threshold down to a single lawmaker, which is what it used to be before Speaker Nancy Pelosi, a California Democrat, changed the rules. Gaetz replied that McCarthy had refused to entertain that idea, but if he is making that offer now, than he would consider it.

McCarthy said he disagreed with Gaetz’s characterization, arguing that the rest of the conference can’t support the threshold as low as one person. “It’s not about me,” the California Republican said. However, he asked Gaetz if he could get to “yes” if McCarthy came down to a one-person threshold, to which Gaetz was still non-committal and said if it was a real offer, he would entertain it.

House rules package

The package released late Sunday includes giving five Republicans the power to call for a vote on deposing the sitting speaker; restoring the ability to zero out a government official’s salary; giving lawmakers 72 hours to a read bill before it comes to the floor; and creating a new select commit to investigative the “weaponization” of the Justice Department and the FBI.

The rules package does not change the process for discharge petitions, which allows lawmakers to circumvent leadership and force a bill to the floor if it has the support of 218 lawmakers.

Other notable items that might be of interest: The rules package prohibits remote hearings and markups, does away with staffer unionization efforts and allows the House Ethics Committee to take ethic complaints from the public.

Rep. Jim McGovern, the current Democratic chairman of the House Rules Committee, called the House GOP’s rules package a “major step backward for this institution.”

“Republican leaders have once again caved to the most extreme members of their own caucus,” the Massachusetts lawmaker said in a statement Sunday.

While the rules package is being billed as final, GOP sources have cautioned that nothing is final until it’s passed.

After the House elects a speaker and swears in members, lawmakers vote on the rules package, which governs how the chamber operates.

This story has been updated with additional developments.