The dysfunctional dance taking place in the House between Speaker Kevin McCarthy and his right flank has driven me to consider something I never imagined possible: that Matt Gaetz is right.

A House speaker can be successful only with the confidence of the members who put him or her in charge, when he or she can follow through on promises made and concessions extracted. Indeed, there may be no job in American government that calls for crackerjack deal-making skills more than that of speaker: so many egos, alliances and grievances to manage to keep things moving.

Mr. McCarthy, in his desperate pursuit of the speakership last winter, ran around making promises willy-nilly to the House’s small band of right-wingers, and he will now rise and fall on how he handles those commitments and expectations. So far, things are not looking good for Kev — and, by extension, for a functional Congress.

Miffed at the speaker’s handling of the spending fight, the right’s hard-liners have been threatening to oust him, shut down the government or both. His attempt to placate them by announcing an impeachment investigation into President Biden went over poorly, prompting multiple Freedom Caucusers to scold him for trying to buy them off. Mr. Gaetz, the Florida congressman and frontman for the rebels who temporarily blocked Mr. McCarthy’s speakership in January, dismissed the move as a disingenuous “baby step,” accused him of being “out of compliance” with his commitments to hard-liners and threatened to force daily votes to vacate the chair — that is, depose him. All of which apparently sent Mr. McCarthy into a profanity laced tirade at a closed-door conference meeting on Thursday that, according to multiple attendees, boiled down to (and here I’ve tidied it up to be family friendly): If you want to file a motion to vacate, file the flipping motion!

The speaker is clearly fed up with being bullied by his radicals. But here’s the thing. Gaetz & Company have a point: Mr. McCarthy is out of compliance with several of his promises — or at least several they claim he made. (That’s the problem with secret back-room deals.) So if the rabble-rousers want to be taken seriously going forward, they need to stop all the chest-thumping. It’s time to step up and file the flipping motion.

The extremists are easy to denounce, especially with their tendency to act out like unruly teens — or Lauren Boebert at “Beetlejuice.” But they are not to blame for the chaos consuming the House. It is Mr. McCarthy who led them to believe he would champion their policies and priorities. And it is Mr. McCarthy who elevated their influence in the conference, empowering them to wreak even greater havoc. Of course they are going to make more and more outrageous demands. That’s what they do.

Some of what Mr. McCarthy committed to was beyond his power to deliver. Take the ongoing showdown over government funding. He pledged to try to cap discretionary spending at 2022 levels or lower. But with the Democrats in control of the Senate and the White House, that is a non-starter. Worse, Mr. McCarthy effectively gave the hard-liners license to play chicken with the debt ceiling. Small wonder they were brassed off when he cut a debt deal with the Democrats in May.

Maybe the key word for Mr. McCarthy in these promises was “try.” Maybe he figured that, as long as he let the rebels take their best shot, they would cut him slack even if they failed to carry the day. If so, their outraged, burn-it-all-down reaction to the debt agreement should have disabused everyone of that notion. At that point, Mr. McCarthy really should have started adjusting his strategy — and the hard-liners’ expectations — accordingly. Instead, he doubled down on coddling them, encouraging them to plow ahead with fantasy spending cuts. The latest proposal for a stopgap bill to keep the government running through October, which the chamber’s G.O.P. leadership put forward on Sunday, was being savaged by around a dozen House Republicans on Monday, dimming its prospects for passage.

Other McCarthy promises involved bits of partisan theater. Mr. Gaetz says the rebels were guaranteed a vote on term limits, something Mr. McCarthy presumably could have arranged time for in the past eight months. But he didn’t. Because he doesn’t give a fig about the radicals’ priorities. He just aims to keep them calm enough for him to keep his gavel.

Am I rooting for the hard-liners to get their way on policy matters such as … well, anything? Good Lord, no. Their revanchist vision for America is not one that I — or a majority of voters for that matter — share. But I get their frustration and anger. Mr. McCarthy created and unleashed this right-wing monster to serve his own ambitions. And yet somehow he seems flummoxed that it is now smashing up things and demanding its due.

Of course, there are practical reasons Gaetz et al. might opt not to boot the speaker. For all their bluster, he may be the best they can hope for. He won’t get them everything they want, but he is willing to be their dancing monkey in plenty of situations. At the same time, he gives the conference enough of a sheen of establishment respectability to retain the support of its non-wingers and to not terrify more moderate voters. Arguably few other House Republicans could or would toe this degrading line.

This speaker is often said to have made a deal with the devil. But the conference’s hard-liners have made one with a cynical, inconstant opportunist. They clearly suspect their slippery chief never intended to deliver on a whole host of stuff they care about, just as they know deep down that an individual so hollow is fundamentally untrustworthy. But until someone is willing to break this stalemate, we are all stuck with their twisted, codependent relationship.