On Tuesday morning, just as the House was returning from its generous late-summer recess, Speaker Kevin McCarthy kicked the fall session off by throwing a bone to conservatives: He was opening an impeachment inquiry into President Joe Biden. This makes it more likely than not—to the extent it was ever unlikely—that House Republicans will impeach Biden, once they can put cobble together the votes and come up with a coherent reason for impeachment.

Why was McCarthy doing this? It’s unlikely that he earnestly believes Joe Biden must be removed from office for high crimes and misdemeanors. No, he was throwing a bone to the far right of his conference, who have been stubbornly threatening to vote against funding the government at the end of the month unless an unreasonable wish list is met. As one Senate Republican put it to the Hill, this was McCarthy “giving people their binkie” ahead of the spending deadline.

But this is not the binkie the hard-liners were looking for.

The Freedom Caucus held a press conference of its own upon returning to Washington on Tuesday afternoon to lay out what it will take to earn their votes for funding the government. Regrettably, for all parties involved, they chose to hold it outdoors in the stubbornly muggy Washington September weather. Press were interspersed with tourists, amateur photographers, and right-wing activists, including several people wearing shirts protesting the “MURDER” of slain Jan. 6 rioter Ashli Babbitt.

The outdoor setting did, however, provide a useful backdrop, as members could point to the Capitol dome to rail against what goes on in “there,” and how they intend to stop it.

The Freedom Caucus has McCarthy over a barrel. McCarthy has said he wants to pass a short-term government funding bill that keeps that lights on until early December to give the House and Senate more time to cut a full-year spending deal. The Freedom Caucus, though, says it won’t vote for a bill that maintains the current rate of overspending for any length of time, whether it’s until early December or for a week. The hard-liners also insist that any spending bill must include House Republicans’ full border security bill, address Department of Justice “weaponization,” and end “woke” Pentagon policies. This presents McCarthy with a choice: Put a “clean” short-term spending bill on the floor that passes with a bipartisan majority—which could (well, would) put McCarthy’s speakership in jeopardy—or join the Freedom Caucus in its display of chest-thumping and steer the government into a shutdown.

At their press conference, one speaker after another—and Lordy, do I mean one after another, when the sun was melting everyone into a puddle—laid out their demands, with no indication that the impeachment announcement had tempered their adamancy.

“Let me be very clear: I will not continue to fund a government at war with the American people,” Texas Rep. Chip Roy, the spicy policy chair of the Freedom Caucus, said.

And which government departments and agencies are the aggressors? It might be easier to ask Chip Roy which ones aren’t. He said the Defense Department is “turning our military into a social engineering experiment wrapped in a uniform.” The Food and Drug Administration is approving COVID boosters for children, “and we haven’t even had clinical trials.” The Inflation Reduction Act is handing out tax credits to “rich leftists” and the “Chinese Communist Party.” The Justice Department is “advancing a politicized form of justice,” targeting “President Trump” and “dads.” And then, of course, there’s the Southern border.

“How many girls have to get sold in the sex trafficking trade before this body”—he pointed at the Capitol—“will wake up and stop an out-of-control president? Enough! Why would we fund that?”

Fellow hard-liners like Freedom Caucus chairman Scott Perry of Pennsylvania, South Carolina Rep. Ralph Norman, Georgia Rep. Andrew Clyde, Virginia Rep. Bob Good—as well as two senators, Utah’s Mike Lee and Florida’s Rick Scott, and heads of various conservative outside groups like the Heritage Foundation, FreedomWorks, Numbers USA, Tea Party Patriots, and Judicial Watch—all drilled down on this: We do not like what the administration is doing, and they must not get the funds to continue doing so.

What I didn’t hear from a single speaker until the Q&A segment, except in a passing reference here or there, was that McCarthy’s escalation of the impeachment process might entice them to vote to keep the government open. Because it won’t. At all.

Don’t get the Freedom Caucus wrong: They think impeaching Biden would be extremely cool. But they view it as separate from the immediate fight to use the power of the purse to box the Biden administration in.

Scott Perry, in taking questions, said the impeachment inquiry has “nothing to do with the debt, the deficit, the outrageous spending, the inflation that’s crushing American families—those are two separate issues, and they should be dealt with separately.”

Bob Good, arguably the most unwavering of McCarthy’s antagonists, said the inquiry announcement had “zero” effect on their demands for the spending bill. North Carolina Rep. Dan Bishop described the inquiry as “irrelevant” to the spending fight.

Is there a way that the two could, arguably, be linked? The specific lever McCarthy would have is to argue that if the government shuts down, so too do the committee impeachment investigations. He’s floated it already, telling Fox News in August that “if we shut down, all the government shuts it down—investigation and everything else.”

The Freedom Caucus doesn’t buy this—and reasonably so. The House won’t be going anywhere in a shutdown, and McCarthy can designate House committee staff as “essential personnel.”

“We’re going to be here, working,” Perry said. “If there’s going to be an impasse in spending, we’re going to be here working on that. So we can walk and chew gum at the same time … we can work on that while we work on the inquiry.” When a reporter asked about whether McCarthy would use the inquiry as leverage—presumably, by sending investigative staff home during a shutdown—Perry said he wasn’t so sure McCarthy would.

“If he’s going to use it as leverage, we’re going to let the American people know that’s the leverage, all right?” Perry said. “I don’t suspect he’s going to do that.”

Impeachment, in short, is not the One Neat Trick to Keep the Government Open. There is no binkie here. To fund the government—whether it’s before or after the shutdown deadline—McCarthy is going to have to put a bill on the floor that doesn’t pass muster with the Freedom Caucus, because it will need to pass a Democratic Senate and be signed by a Democratic president. And yes, that will likely prompt some of those openly threatening to put McCarthy’s speakership up to another vote to go through with it. Florida Rep. Matt Gaetz, who gave a separate floor speech Tuesday putting McCarthy on notice, told reporters that he would move to vacate the chair if McCarthy puts any short-term spending bill on the floor, according to Bloomberg.

Perhaps McCarthy should get the inevitable ouster attempt out of the way. He’d have options—grinding down the Republican opposition again, as he did in January; turning to Democrats to bail him out (though the impeachment flailing may have restricted this path); retiring to a K Street sinecure and letting the next hapless schmo serve an eight-month speaker stint. If you’re at the point of launching an impeachment inquiry as a political decoy to (not) get through a short-term legislative problem, it might be time to force the bigger question.