House Republicans opposing Minority Leader Kevin McCarthy's endangered bid for speaker say he's not agreeing to their demands, which include significant changes in how the GOP conference operates and major spending cuts. 

They say they're prepared to vote against his candidacy for speaker on the House floor on Jan. 3 if McCarthy, R-Calif., doesn't cede to their demands, and they claim there are several other Republicans who will do the same. 

"Miracles do happen," Rep. Ralph Norman, R-S.C., said when asked if there is any chance he'd vote for McCarthy. "I am a hard no. I am willing to listen for the next 33 days... I'm anxious to listen. I went to a meeting yesterday where we listened."

"If it's just [changes to House] rules, no," Norman told Fox News Digital. "It's going to have to be more substantive than just rules. Rules can be waived… He's going to have to give an ironclad… agreement that we will have a budget that will balance. If not in seven years, give me a timeframe."

Kevin McCarthy speaks

House Minority Leader Kevin McCarthy, R-Calif., aims to be the next speaker. (REUTERS/Jonathan Ernst)

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Norman continued that McCarthy should tell committee chairs, "This is what we've got to have, cuts we've got to have. And if you don't do that, all of a sudden your chairmanship may be in jeopardy."

Norman is joined by Rep. Andy Biggs, R-Ariz., who says he's going to challenge McCarthy on the House floor on Jan. 3., and Reps. Bob Good, R-Va.; Matt Rosendale, R-Mont.; and Matt Gaetz, R-Fla.

Good said it is "good news" that "the leadership challenge has encouraged the leadership to consider some changes that need to be made to how Congress operates." But, he added, there are significant sticking points that remain, including bringing back the motion to vacate the chair, enacting a "majority of the majority" rule and retuning legislation to regular order through committees.

Rosendale also told Fox News Digital he does not support McCarthy at this point.

"I have not seen any change in his stance that would earn my support," Rosendale said. "There's a group of us that presented Kevin McCarthy a list of amendments that we wanted to the House rules and to the conference rules four months ago."

FILE - In this Tuesday, June 20, 2017, file photo, Republican Ralph Norman speaks to supporters at a campaign party in Rock Hill, S.C., after winning South Carolina's 5th Congressional District. Norman pulled out his own loaded handgun during a meeting with constituents Friday, April 6, 2018, to make a point that guns are dangerous only in the hands of criminals. (AP Photo/Chuck Burton, File)

Rep. Ralph Norman, R-S.C., opposes Rep. Kevin McCarthy, R-Calif., for speaker. (Associated Press)

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"Interestingly, since the election, he's been much more interested in talking to us," he continued. "They have not made enough progress… to change my stance whatsoever."

McCarthy and his allies say they're confident that he will have the votes on the House floor, and they have over a month left to figure out how to reach 218, which would give him the support he needs — more than half the House. 

Among McCarthy's boosters, notably, are high-profile House Freedom Caucus members Rep. Majorie Taylor Greene, R-Ga., and Jim Jordan, R-Ohio.

Some Republicans have criticized those opposing McCarthy, alleging that they are highlighting a divide in the party when the focus should be on unifying. McCarthy, meanwhile, said on Newsmax this week that Democrats could influence the choice of speaker if conservatives don't put down their opposition. 

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But Good called the idea of bipartisan cooperation on a speaker "intentional disinformation." 

Bob Good headshot

Rep.-elect Bob Good, R-Va., says he will vote for a candidate besides Rep. Kevin McCarthy, R-Calif., for speaker on Jan. 3. (Bob Good campaign)

"Tell me [which] Republicans are going to work with Democrats to elect a speaker," Good said. "No Republicans are going to work with Democrats to elect a speaker."

Thirty-six members voted against McCarthy in a House GOP conference vote earlier this month. And if the group currently publicly opposing McCarthy remains united, they likely could sink his speakership bid due to the GOP's minuscule majority. Good reiterated to Fox News Digital that he will vote against McCarthy on the House floor. 

"I will not be voting for Kevin McCarthy. I'll be voting for an alternative candidate on January 3," Good said. "I said when I ran that I would evaluate him based on what he did in his first two years… there wasn't anything during my first two years that gave me the confidence."

Good said McCarthy wasn't "using every tool at our disposal to fight against the Democratic majority."

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"Andy Biggs said he believes that hard-no numbers about 20. I think he's in the ballpark," Good said. "I think it's gonna be a lot more than people think. What we need is someone who's in the conservative center of the conference… that has to demonstrate toughness and willingness to fight to block what the Senate is doing under Schumer, to block what Biden is trying to do." 

McCarthy's office did not immediately respond to a request for comment. 

Fox News' Sally Persons and Kelly Phares contributed to this report.