The final hurdle to Republican Kevin McCarthy’s years-long quest to secure the speaker’s gavel grew even more formidable on Monday as a sizable group of House colleagues from his own party said they were not yet ready to support him.

The nine Republican rebels made the announcement after the California congressman made a series of concessions on Sunday to try to shore up the support of conservative hardliners ahead of Republicans assuming control of the US lower chamber on Tuesday.

McCarthy can afford to lose only four votes from his party’s slender majority if he is to win the election for speaker that will be among the first orders of business for the new Congress.

The rightwingers had demanded a change in House rules to make it easier to topple the speaker, and increased representation for fringe members on committees.

While the group’s statement acknowledged there had been some steps forward, it said McCarthy’s messaging during a Sunday evening conference call, and in a summary sheet obtained by Punchbowl News, left them uncertain of exactly what he was offering.

“Despite some progress achieved, Mr McCarthy’s statement comes almost impossibly late to address continued deficiencies,” the letter, signed by the Pennsylvania congressman Scott Perry and eight colleagues, said, according to Politico.

“Expressions of vague hopes reflected in far too many of the crucial points still under debate are insufficient.

“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.”

McCarthy published a 55-page package of proposed rules on Sunday as he attempted to secure the 218 votes he will need to become speaker.

The main sticking point appears to be the so-called motion to vacate, a House rule that allows members to challenge the speaker, which was loosened during the tenure of the Democrat Nancy Pelosi.

The hardliners want a restoration of the rule that existed under previous Republican speakers John Boehner and Paul Ryan that any single congressman or woman could initiate a vote to remove the speaker.

McCarthy said in his call on Sunday that “weeks of negotiations” had resulted in a “concession” of him agreeing to a threshold of five House members.

But according to CNN, it was not enough to appease Republicans known as “Never Kevins”, a fluid group of hardliners including the Florida congressman Matt Gaetz, who have said they will not support him under any circumstance.

The network reported that later in McCarthy’s call, Gaetz said he would “consider” any offer to lower the motion to vacate threshold to one, but that he did not believe it was being made.

McCarthy, CNN said, told Gaetz that the rest of the Republican conference would not support such a move. “It’s not about me,” McCarthy is reported to have said.

Other proposals by McCarthy would give lawmakers a minimum 72 hours to read a bill before it comes to the floor, and another concession to rightwingers of creating a select committee to investigate the “weaponization” of the FBI and justice department.

A disappointing performance for Republicans in November’s midterms created a particularly rocky path to the speakership for McCarthy, whose most recent challenger for the gavel ended in defeat to Ryan in 2015.

Democrats, and some Republican moderates, have accused McCarthy of caving to extremists and placing his own personal political ambitions ahead of the good of his party.

In an interview with the Guardian last week, John Yarmuth, outgoing chair of the House budget committee, said the Republican party had become so extreme that it would be willing to default on US debt for the first time in an attempt to secure concessions from Joe Biden’s administration.

“My guess is that whoever is speaker of the House will be so in a vice from the extreme members of their caucus, that they won’t be able to get anything done here. I really worry about defaulting,” Yarmuth, a Kentucky Democrat, said.

In a statement on Sunday, the Massachusetts Democrat Jim McGovern, chair of the House rules committee, attacked McCarthy’s proposals as a “major step backward”.

“Republican leaders have once again caved to the most extreme members of their own caucus,” he wrote.

And in an interview with CNN’s State of the Union on Sunday, Republican Adam Kinzinger of Illinois, who is standing down from the House, said McCarthy’s refusal to confront Donald Trump’s election lies had allowed extremism to thrive.

“He is the reason Donald Trump is still a factor. He is the reason that some of the crazy elements of the House still exist, Kinzinger said.

McCarthy’s allies say there is still time to negotiate the rules package. The House will vote on it later in the week after a speaker is elected and sworn in.