After five days of chaos and 15 rounds of floor votes, newly elected Republican House speaker Kevin McCarthy is set to face an instant challenge on Monday as the House votes on a new rules package.

A handful of establishment Republicans indicated on Sunday they may withhold their support for the rules unless more details of concessions made to ultraconservative lawmakers during a week of torrid negotiations are unveiled.

McCarthy ascended to the speakership late on Friday after winning over support from holdout members of the hard-right freedom caucus who had leveraged their power due to the slim margin of control Republicans hold in the House.

But full details of those negotiations have not been made public, leading to speculation that McCarthy has guaranteed the group positions on key committees and thrust them further into power.

Speaking to CBS News on Sunday congresswoman Nancy Mace, a more moderate Republican from South Carolina, said while she supported the package itself, she had not decided on whether to vote for it on Monday.

“My question really is today: what backroom deals did they try to cut, and did they get those?” Mace said, with reference to the holdout lawmakers.

She added: “We don’t know what they got, we haven’t seen it. We don’t have any idea what… gentleman’s handshakes were made. And it does give me a little bit of heartburn because that’s not what we ran on.”

The package itself was published on Friday evening, and includes a measure to allow a single member to force a “motion to vacate” the speakership, already weakening McCarthy’s position, and a key demand of the holdout conservatives. It also includes reinstating a provision to allow lawmakers to propose amendments to appropriations bills, adds a 72-hour window for members to read bills before they vote, and a commitment to vote on legislation on term limits for members of Congress.

But anonymous briefings have indicated that the holdout Republicans also attempted to negotiate more leverage over key committees, including approvals over a third of positions on the powerful rules committee, which is responsible for what proposed legislation reaches the floor of the House.

On Sunday, Republican congressman Tony Gonzales of Texas told CBS he would vote against the rules, citing disagreements with potential spending cuts to the defense department, which he described as a “horrible idea”.

Gonzales said he was not urging other members to also vote against the rules, but cautioned that last week’s tumult within the party, was “only the beginning”.

“Republicans are much different than Democrats,” Gonzales said. “We’re not just going to line up and jump off the cliff. All of us represent our districts and we’re gonna fight for that.”

One of the central figures in negotiations between the ultra-conservatives and McCarthy was Texas congressman Chip Roy who acknowledged on Sunday that negotiations included adding more freedom caucus members to influential committees but did not provide further details.

Speaking to CNN Roy said: “It’s not about petty personal desires. I don’t want to be on the Rules committee. I don’t want to leave my family on Sunday night and miss my kids, to come up here (Washington DC). But I might do it if that’s what my colleagues decide.”

The divisions highlight the dilemmas posed by such a slim Republican majority in the House. But speaking on Sunday, Jim Jordan, a freedom caucus member and the expected new chair of the House judiciary committee, predicted the rules package would pass on Monday and defended the chaos of last week.

“Sometimes democracy is messy, but I would argue that’s how the founders intended it,” Jordan told Fox News. “They wanted real debate, real input from all people and then you get a decision, whether it’s one vote or 15 votes, Kevin McCarthy is still speaker of the House.”

The House judiciary committee, under Jordan’s leadership, is expected to launch a highly charged investigation into the US justice department over purported allegations of political bias, partly in relation to its ongoing inquiry of the January 6 insurrection.

But a number of Republican lawmakers have been implicated in the investigation themselves, leaving open questions around conflicts of interest.

On Sunday, the House freedom caucus chair Scott Perry, one of those under investigation, argued he could still serve on a committee undertaking oversight of federal investigators.

“Should everybody in Congress that disagrees with somebody be barred from doing the oversight and investigative powers that Congress has?” Perry told ABC News, adding: “I get accused of all kinds of things every single day, as does every member that serves in the public eye.”