On the surface, House Speaker Kevin McCarthy has reason to be pleased. He and his team negotiated a budget deal with the White House; they extorted some Democratic concessions; and their legislation appears on track to pass the GOP-led House today, after clearing the Rules Committee late yesterday. The plan — which includes avoiding a catastrophic default — appears to be on track.

But just below the surface, the California Republican has a related problem that won’t be resolved by the passage of a bill.

Members of the House’s most far-right contingent, the House Freedom Caucus, were under the impression that they were driving the debt ceiling process. It was, after all, their radical plan that passed the chamber last month, and McCarthy reportedly told this faction that he’d fight to secure their regressive priorities.

As the Fiscal Responsibility Act advances, and the Freedom Caucus realizes that practically all of its goals were discarded during the bipartisan negotiations, these House Republicans are not content to simply vote against the bill. Politico reported yesterday:

Conservative angst over the debt deal is threatening to trigger Kevin McCarthy’s biggest fear — a push to oust him from the speakership. Rep. Dan Bishop (R-N.C.) on Tuesday became the first House conservative to explicitly state he is considering a push to strip McCarthy of the gavel over his recent deal with President Joe Biden.

Asked if he’s prepared to use procedural tactics to force a vote on McCarthy’s future, the North Carolina Republican told Politico, “Absolutely. It is inescapable to me. It has to be done.”

He appears to have some company within the GOP conference. Rep. Ken Buck of Colorado broached the subject during a House Freedom Caucus conference call yesterday, and told NBC News yesterday that he raised the possibility “as a result of a broken promise.”

Rep. Scott Perry, the contingent’s current chair, didn’t explicitly endorse moving against McCarthy, but the Pennsylvanian didn’t rule out the possibility, either.

Rep. Chip Roy didn’t call out McCarthy by name, but the Texan declared at a Capitol Hill press conference, “We will continue to fight it today, tomorrow, and no matter what happens, there’s going to be a reckoning about what just occurred.”

He also appeared on Glenn Beck’s program yesterday, adding, “If we can’t kill it, we’re going to have to regroup and figure out the whole leadership arrangement again.”

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For his part, Rep. Matt Gaetz, as recently as a few days ago, downplayed the possibility of trying to take down McCarthy, but yesterday the Florida Republican told CNN that if the bipartisan agreement is opposed by a majority of House Republicans, and it passes anyway thanks to Democratic support, that would “likely trigger” an immediate vote against McCarthy.

Let’s not forget what makes such talk relevant: As we discussed last week, as the new Congress got underway, and McCarthy was begging his own members for their support during his protracted fight for the speaker’s gavel, he agreed to tweak the motion-to-vacate-the-chair rules, which at least in theory, would make it easier for angry House Republicans to try to oust McCarthy from his leadership position.

And now some of his members are being unsubtle about their interest in just such an attempt.

As a matter of legislative arithmetic, the House speaker probably isn’t too worried: Even if Freedom Caucus members held what is effectively a no-confidence vote in McCarthy, the vote would very likely fail. For one thing, the far-right rage appears to be relatively limited. For another, it’s possible, if not likely, that some House Democrats would help save McCarthy under such a scenario, fearing that his successor would be worse.

But the larger point is that the House speaker, already perceived as weak, may soon have yet another headache on his hands, thanks to a backlash from some of his own members.