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Conservative critics of Speaker Mike Johnson’s leadership are warning that he has an uphill climb to winning back their support in time for House Republicans’ leadership elections at the end of this year.

"He's gonna have a tough time based on past history, because I would submit he's failed on just about everything other than initiating [the Homeland Security Secretary Alejandro Mayorkas] impeachment effort," House Freedom Caucus Chairman Bob Good, R-Va., told Fox News Digital.

Johnson was elected speaker in October in a strongly unanimous House GOP vote, with Republicans hungry for unity after three weeks of turmoil following ex-Speaker Kevin McCarthy’s ouster.

The Louisiana Republican now finds himself in a similar situation to his predecessor, with a small but vocal group of lawmakers on his right flank calling for his immediate removal, through a process known as motion to vacate, for working along bipartisan lines on critical legislation. The push is being made by Reps. Marjorie Taylor Greene, R-Ga.; Thomas Massie, R-Ky.; and Paul Gosar, R-Ariz.

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Chip Roy, Mike Johnson, Bob Good

House Freedom Caucus members like Chip Roy, left, and Bob Good, right, and their allies are signaling that Speaker Johnson, center, will have to work hard to get their support in the next leadership election. (Getty Images)

The vast majority of House Republicans have refused to take up that fight again, but Republicans angry over what they see as Johnson’s failure to deliver on conservative priorities like border security and cutting federal spending signal he has miles of ground to recover before they back him a second time.

"Whoever wants to be in any leadership position for the Republican House of Representatives should we be blessed to be given the majority again, which is going to take a c--- ton of hard work between now and November, is going to have to demonstrate not only the policy direction they want to, but the track record and willingness to stand up and fight for it. And, so far, we have not delivered what we need to deliver," said Rep. Chip Roy, R-Texas.

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Good was one of eight House Republicans who voted with Democrats to oust McCarthy last year. He distanced himself from calls to immediately remove Johnson last week, citing the much slimmer House majority Johnson is operating with. But Good suggested he wanted to see new leadership races in November after the election.

He told Fox News Digital Monday his support for Johnson would hinge on his handling of fiscal year 2025 appropriations, the deadline for which is Sept. 30.

"He could truly fight for Republican policy initiatives. He could truly fight to cut our spending. He could fight to ensure that we do not fund the government unless it reflects Republican priorities," Good said. "He has sort of one more big crack at the bat. I hope he'll take that opportunity."

Johnson and Congressional appropriators are headed into that fight with their hands relatively tied by the Fiscal Responsibility Act, the deal to raise the debt limit struck by McCarthy and President Biden last year, which also set certain terms on shaping fiscal year 2025 funding priorities.

House Speaker Kevin McCarthy in the U.S. Capitol

Johnson took over after House Speaker Kevin McCarthy, pictured, was ousted. (Al Drago/Bloomberg via Getty Image)

A spokesperson for Johnson told Fox News Digital, "Speaker Johnson is committed to governing – not his political ambitions. He will continue to advance conservative priorities and demonstrate how we’ll grow our majority in November."

Party leadership races are normally held behind closed doors in the weeks after an election. If Republicans keep the House, Johnson would traditionally only need a majority vote there to then prevail as speaker on the House floor, with fellow Republicans expected to get in line even if they didn’t support him initially.

But the 15 rounds McCarthy went through last year, repeatedly blocked by GOP dissent, show that Johnson may need to guarantee unanimous support behind closed doors even if he manages to keep Republicans in power.

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"Moving forward, I would ask Mike Johnson if being speaker is something he wants to continue. If he is, I would have an all inclusive list of issues where he would agree/not agree to actually make happen as speaker BEFORE I would commit," Rep. Ralph Norman, R-S.C., said via text message.

Norman and Good were two of the original McCarthy holdouts

Rep. Ralph Norman

Rep. Ralph Norman said he would need certain guarantees from Johnson to support him. (Saul Loeb/AFP via Getty Images)

"Based on his past performance, I doubt he would agree to take the hard negotiation stance that I would need to see. However, due to my respect that I have for Mike as a person, I would start with the questions as listed," Norman said.

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Rep. Tim Burchett, R-Tenn., who voted to oust McCarthy in October, said he was "open to discussion" about supporting Johnson, but he needed to see "a clear plan for fiscal responsibility" and border security.

Roy, however, was less optimistic House Republicans would see wins in the end-of-year spending fight. 

"There will not be, in my opinion, under this leadership, and in this environment, at this time, the ability to move or ration bills before Election Day that are going to drive the policy that needs to be driven," the Texas Republican said.

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