Less than a week away from a government shutdown, Speaker John A. Boehner seems to have two core goals: Keep the government open and hang on to his gavel in the process.

The Ohio Republican will somehow have to persuade the rowdier corners of his conference that shuttering the federal government over Planned Parenthood funding isn’t in the GOP’s best interest, while also convincing critics he’s still the best person to lead the conference as Republicans and Democrats potentially negotiate a massive spending bill this fall.

Hanging over Boehner’s head is a resolution to remove him as speaker. And while a number of conservatives say there is no plan for a privileged motion that would force a vote on Boehner, many members expect such a vote is likely to follow on the heels of any continuing resolution that funds Planned Parenthood. (GOP leadership could pre-empt that move by bringing up North Carolina Rep. Mark Meadows’ resolution to table it.)

GOP leaders are scheduled to meet after Pope Francis’ address to Congress Thursday, and a Democratic source told CQ Roll Call some offices have heard it’s possible the House votes on a continuing resolution this week, as well on a motion relating to the Meadows resolution.

That the resolution to remove Boehner has hung out there this long already has emboldened conservatives. Thomas Massie, R-Ky., said he doesn’t expect Boehner to survive much longer, partly because, “I think the speaker assumed that outcome when they decided not to call the vote [on the resolution to remove Boehner] the day before recess,” just hours after Meadows initially offered the resolution.

But Boehner has been emphatic he’s staying put. “Writing the same story over and over again isn’t going to change the fact that the speaker isn’t going anywhere,” Emily Schillinger, Boehner’s spokeswoman, told CQ Roll Call this week.

And as much as conservatives talk about taking down the speaker, they still don’t have a clear plan beyond hoping Boehner resigns.

The most sophisticated plot seems to consist of little more than calling for a vote on a motion to vacate the chair; getting enough Republicans to vote against Boehner that he requires support from Democrats; then arguing the Ohio Republican is in no position to remain the No. 1 Republican when Democrats could call for a vote at any moment and end his speakership with the coalition of anti-Boehner Republicans.

That strategy, as well as the general frustration with conservatives in the Republican Conference, prompted a close Boehner ally, Intelligence Chairman Devin Nunes of California, to tell The Hill, “The right-wing Marxists have teamed up with Pelosi.”

That comment is sure to fire up conservatives even more, and it could be used as fodder to stoke up the base against establishment Republicans — a tactic that almost certainly would be necessary for a Boehner coup to actually work.

The argument that Boehner can’t effectively lead congressional Republicans without their near-universal support would most likely rely heavily on outside conservatives, perhaps even 2016 presidential candidates, mobilizing against Boehner. That’s a possibility for some candidates, but it’s another variable in a coup that could fail at any step.

Another strategy from conservatives seems to be hoping that other GOP leaders, and would-be leaders, push Boehner to the exits. It’s not so much that conservatives believe Republicans such as Majority Leader Kevin McCarthy would participate in an effort to ditch Boehner, but they say that, with Boehner gone, they see an opportunity to strike up a coalition with McCarthy where he takes the speakership and one of their own, such as House Freedom Caucus Chairman Jim Jordan or Raúl R. Labrador, takes majority leader.

One HFC member said Jordan talked to him about eventually supporting McCarthy for speaker.

But if Jordan or Labrador are the chosen conservative leadership candidates, both are doing a convincing job of dismissing that gossip. They have told CQ Roll Call those efforts just aren’t happening. And other conservatives agree the scenario is far-fetched.

“I think if you bargain for that, you’re going to get something much worse,” Massie said.

Instead, Massie’s push is for Florida’s Daniel Webster — the middle-of-the-road Republican who garnered 12 speaker votes in January and was then promptly removed from the Rules Committee.

Webster’s run for speaker was based not on his personal politics, but on changing the process by which Republicans in Congress operate. He wanted to make the lawmaking process more inclusive. While that message may resonate with a majority in the GOP conference, it’s difficult to imagine a scenario where Webster — let alone anyone other than Boehner — could actually win the speakership.

Without a clear candidate, the already long odds of taking down Boehner get even longer. Similar efforts to take down Boehner have failed in the past because conservatives couldn’t find a viable alternative. That may be why conservatives have seemed surprisingly open to the idea of McCarthy taking the speakership — as long as one of their own takes majority leader.

“There are circumstances in which I can vote for any member of the GOP conference for speaker,” Rep. Mo Brooks, R-Ala., told CQ Roll Call late last week. “You’d have to look at the entire team, not just one member of the team.”

But as much chatter as there is about Boehner losing his job, Brooks still thinks Boehner’s speakership is safe, mostly because Brooks assumes that Democrats’ “first inclination” would be to abstain from a vote on a motion to vacate the chair. In that scenario, it would take more than 120 Republicans to vote against Boehner — and Brooks just doesn’t see how that would happen.

“All this talk is kind of rumor mill and gossipy, but until there’s 124 votes, there’s no substance to it,” Brooks said.

Emma Dumain contributed to this report.

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