Is it just me, or did Kevin McCarthy look a little rough around the edges on Tuesday when announcing his decision to open an impeachment investigation into President Biden?

I realize that Mr. McCarthy, the House speaker, needed to convey a dignified solemnity on such an occasion. “I do not make this decision lightly,” he assured the American people as he tried to make an argument about a “culture of corruption” and the president maybe lying about his son’s sketchy business dealings. But in his brief appearance, Mr. McCarthy came across not so much as serious and statesmanlike but as if the words were being dragged from his lips.

It may be that even he is nauseated by his latest stunt. That it has finally sunk in that he has become the not-so-glorified puppet of the House Republican conference’s radicals, folks like Dan Bishop, Chip Roy and, most prominently, Matt Gaetz.

Mr. McCarthy may wield the gavel. But the far-right rebels who opposed his election as speaker, of whom Mr. Gaetz was a ringleader, now wield the ax poised above Mr. McCarthy’s exposed neck — an ax that he handed them in exchange for them letting him pretend to be in charge. With the omnipresent threat of voting him out of his dream job, the conference’s fringe is leading the speaker around by the nose hairs. And whenever they feel he’s getting a bit sassy, they give those hairs a sharp yank.

It’s the kind of grinding, demeaning situation that can really wear a guy down.

To some degree, wrangling the rabble-rousers is always a feature of the speakership. Paul Ryan had to make his peace with the ultraconservative, ultradisruptive Freedom Caucusers who had essentially driven his predecessor, John Boehner, out of the job. And Nancy Pelosi had her share of tussles with the Democratic caucus’s left wing.

But Mr. McCarthy is in an especially ticklish position, in part because of his emaciated majority and in part because of the various promises and concessions he made to the hard-liners during the speaker’s race. (Multiple wing nuts on the Rules Committee? A return to allowing an individual member to force a vote to dethrone the speaker? Woof.)

Pretty much everyone acknowledges that this isn’t how Mr. McCarthy wanted the impeachment thing to go. As a political animal, he knows that a slipshod, nakedly partisan impeachment inquiry started without compelling evidence threatens the electoral fortunes of his members from more moderate areas — including the 18 who represent districts that went for Mr. Biden in 2020. The non-wingers don’t want to be mired in an impeachment circus heading into next year’s electoral scrum, and they most likely would not have voted to approve one.

But the moderates do not call the shots in this Republican conference. Which is why Mr. McCarthy executed a trademark flip-flop, unilaterally ordering up an investigation without a vote even though he had recently asserted that such a vote was required. This bit of hypocrisy promises to be awkward since, in January 2020, the Trump Justice Department ruled that impeachment investigations by the House are invalid without a formal authorization vote. But Mr. McCarthy is desperate to placate the wing nuts.

Gaetz & Company have been threatening to oust Mr. McCarthy if he doesn’t meet their (outrageous) demands in the looming spending battle, and he is hoping that a good impeachment romp will focus their twitchiness elsewhere. This is a bold bet: The hard-liners are still super salty about the debt-ceiling deal Mr. McCarthy cut with Democrats in May.

Indeed, Mr. McCarthy had barely wrapped up his impeachment dirge when Mr. Gaetz took to the House floor to dismiss the speaker’s “rushed and somewhat rattled performance” as malarkey and to stress that the hard-liners will not be so cheaply bought. If Mr. McCarthy cannot be brought into “immediate, total” compliance with the promises he has made the rebels, he asserted, they will have no choice but to take his gavel.

Mr. Gaetz went on to list the myriad ways in which Mr. McCarthy has vexed his right flank, including declining to hold a vote on term limits or on balanced budgets, failing to arrange a “full release” of the Jan. 6 tapes, refusing to get serious about slashing spending. Mr. Gaetz heaped special scorn upon the debt deal, charging Mr. McCarthy with “serving as the valet” to advance the president’s “spending agenda.”

This makes for a hefty (read: impossible) to-do list, and one can only assume Mr. Gaetz is willing to be flexible in his definition of “immediate.” But his basic message to the speaker was clearer than a shot of Stoli: We own you, buddy, so get busy making us happy. Or else.

Mr. McCarthy’s impeachment caper is just the most garish example of the impossible power dynamic he has saddled himself with. An arguably more pathetic case was the speed with which he backpedaled on the debt agreement that was by far his biggest leadership win. After the deal passed, Mr. McCarthy got to bask for only a few days in the glow of competence before a gaggle of outraged hard-liners, again fronted by Mr. Gaetz, shut down business on House floor in protest over the agreement.

For several days, the mutineers held the House hostage while they negotiated with Mr. McCarthy for … well, it’s hard to say for sure. But next thing you know, the speaker had effectively abandoned his own deal, embracing the nonsensical position that its spending levels were a ceiling rather than a target and that Republicans would be writing bills with lower limits. The House and Senate are expected to spend the next weeks or even months locked in a nasty fight over how to reconcile this mess.

Mr. McCarthy’s hard-liners intend to make things as bloody as possible. On Tuesday afternoon, members of the Freedom Caucus held a press event to warn that they will not back a stopgap resolution to fund the government past Sept. 30 unless their policy demands are met. They emphasized that Mr. McCarthy’s impeachment announcement means squat when it comes to the spending fight. “Him starting an impeachment inquiry gives him no — zero — cushion,” asserted Bob Good of Virginia.

Mr. Gaetz has gone even further, teasing reporters that votes to oust the speaker could become a daily occurrence: “If we have to begin every single day in Congress with the prayer, the pledge and the motion to vacate, then so be it.”

Mr. McCarthy is a slippery enough operator that he may wriggle his way out of this jam. “Live to fight another day” seems to be his guiding principle. Which is probably the most he can hope for, since there appears to be no good way out of his toxic relationship with his hard-liners. They will never be satisfied. And he will always be under imminent threat of losing the job for which he long ago sold his soul.

So much stress and blame, so little real authority. It’s a wonder Mr. McCarthy even wants this lousy, thankless, increasingly hollow gig — or what he hopes to accomplish.

So much more satisfying to be someone like Mr. Gaetz. He doesn’t need to be the speaker. He has the speaker running scared.