Speaker Kevin McCarthy appears to have reached an agreement with conservatives about easing their blockade of the House floor that sent lawmakers home early last week. 

A group of 11 conservatives, furious with how McCarthy, R-Calif., handled debt limit negotiations with President Biden, upended a normally sleepy procedural vote on Tuesday and blocked Republican bills aimed at protecting gas stoves. It was the first time in two decades that a majority party watched its own members vote with the minority to defeat a bill at that procedural stage.

They also accused GOP leadership of threatening Rep. Andrew Clyde, R-Ga., by blocking his pro-Second Amendment legislation from the House floor because of his earlier efforts to take down the debt limit bill. That bill, aimed at rolling back a Biden administration provision on pistol braces, is scheduled for a vote tomorrow.

But it appears relations have thawed since last week after House lawmakers left for an early recess on Wednesday. Rep. Ralph Norman, R-S.C., told reporters on Monday evening that he believes the chamber will move forward on a combined procedural vote paving the way both the gas stove bills as well as Clyde’s resolution.

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Rep. Ralph Norman, R-S.C., and members of the House Freedom Caucus hold their news conference to oppose the debt limit deal outside the US Capitol on May 30, 2023. (Bill Clark/CQ-Roll Call, Inc via Getty Images)

"Yes," Norman said when asked if all 11 holdouts would let vote pass. "Well, I can’t speak for everybody. Ask them. My inclination is yes."

He explained earlier, "We aired our issues. We want to see this move forward as a body…there’s a lot of fights down the road that we’d rather be on together."

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Norman indicated McCarthy "listened" to their concerns and "would involve more of us in the discussions" but hinted at lingering frustration over the debt limit compromise. He added that the ongoing discussions on spending, going on over the upcoming appropriations process, were "a work in progress."

McCarthy said there would be no votes on Monday evening but "we're going to combine the rule tomorrow, take up the rule and move forward."

House Speaker Kevin McCarthy

Speaker of the House Kevin McCarthy, R-Calif., talks to reporters just after the Republican majority in the House narrowly passed a sweeping debt ceiling package as they try to push President Joe Biden into negotiations on federal spending, at the Capitol in Washington, Wednesday, April 26, 2023.  (AP Photo/J. Scott Applewhite)

"I thought we had a very productive meeting tonight," he added. "I think everybody's attitude in the room was, how do we move forward? How do we move forward to where we were with our strength together? And I think there's a willingness, that doesn't mean it's all locked together, it means that we thought that meeting was great…we've got a lot more victories for the American people."

Rep. Bob Good, R-Va., another of the GOP rebels, told reporters, "I think you’re going to see an agreement to move forward in the next day or two on moving the legislation we wanted to move last week."

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A GOP lawmaker told Fox News Digital earlier on Monday that conservatives are seeking two key assurances from McCarthy in the upcoming appropriations process, when the House Committee on Appropriations will consider 12 separate spending bills for the next fiscal year. One is a promise to cap federal spending at fiscal year 2022 levels, which is below the limit agreed upon by McCarthy and Biden in the bipartisan Fiscal Responsibility Act.

A 2022 spending cap was the GOP’s original goal when it passed its first debt limit bill, the Limit, Save, Grow Act, along party lines in April. Several conservatives staging the blockade, who also voted against the bipartisan compromise, indicated that they view anything less than the GOP bill as a loss.

WASHINGTON, DC - MARCH 10: Rep. Bob Goods (R-VA) speaks during a news conference with the House Freedom Caucus on the debt limit negotiations at the U.S. Capitol Building on March 10, 2023 in Washington, DC. Members of the caucus held the news conference to say they would consider voting to raise the debt ceiling in exchange for enacting legislation that would "shrink Washington" and bring government spending back to before 2020 and the Covid-19 Pandemic. (Photo by Anna Moneymaker/Getty Images)

WASHINGTON, DC - MARCH 10: Rep. Bob Good (R-Va.) speaks during a news conference with the House Freedom Caucus on the debt limit negotiations at the U.S. Capitol Building on March 10, 2023, in Washington, DC.  (Anna Moneymaker/Getty Images)

GOP rebels also want a commitment to stop spending on programs whose authorization has run out, a point Rep. Ken Buck, R-Colo., reiterated over the weekend.

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"We have 11,118 programs, OK, 11,118 programs that are unauthorized in the federal government… It means when they passed a program like the Endangered Species Act of 1973, it had a five-year sunset on it. It went down, finished, over in five years unless it was reauthorized. So in 1978, it was reauthorized. It has not been reauthorized since, and every year we increase the spending to the Endangered Species Act," Buck explained in a speech over the weekend.

"We have a House rule that we pass every Congress, Republicans and Democrats, you can't appropriate money to an unauthorized program… We waive that rule in every appropriations bill," he said.

Brianna O'Neil contributed to this report