Speaker John Boehner appears to have had it with the far-right faction of about 45 congressmen who have repeatedly undercut his leadership. Asked by a reporter last week if he had a plan to avert the looming budget crisis, Boehner let his frustration show, replying, "Why don't you give me one so they can shoot it down too?" A few days earlier, reports surfaced that Boehner may just quit after next year's midterm elections.

Then again, this week, Boehner has given in to the far right's ludicrous demands, by backing a plan that would keep the government open only if ObamaCare is repealed. He also proposed a debt limit increase stuffed with every poison pill imaginable. If Boehner remains beholden to his extremists, the resulting stalemate with the Senate would cause both a government shutdown and an economically devastating debt default.

Such a small minority faction can give Boehner agita because Boehner won the speaker's gavel with only six votes to spare. In theory, he could pass lots of bills on a bipartisan basis without those 45 or so conservative votes, even without the votes of a majority of the Republican caucus. He has already done so a few times this year at critical moments, but only after weeks of brinksmanship. Every additional time he reaches across the aisle and snubs the "majority of the majority," Boehner increases the risk of becoming the victim of a coup.

At the same time, Boehner has long made his view clear to his fellow Republicans that a government shutdown or a debt default must be avoided because it could lead to election losses next year and the end of Republican control of the House.

Boehner appears stuck between a rock and a Tea Party. Indeed, The Washington Post's liberal political analyst Greg Sargent predicts, "At some point this fall, Boehner will have to cut the Tea Party loose, and suffer the consequences."

But that's not quite right. Yes, Boehner can't let the Tea Party tail wag the Republican dog forever without destroying the global economy. But no, he need not suffer the loss of his gavel.

Despite his most recent provocation, Boehner will eventually have to allow a final bipartisan compromise to reach the floor, whether or not a government shutdown or debt default occurs first. If after that the irreconcilable right wants to embark on a coup, it doesn't get to simply take Boehner out to a back alley, dispose of him, and replace him with Michele Bachmann.

Under the House's parliamentary procedure, a "resolution declaring the Office of Speaker vacant" must be brought to the full House for all members to vote on. Everyone. Republican and Democrat.

For the resolution to pass, either a nearly unified Republican caucus would have to agree to dump Boehner — an extremely unlikely scenario — or a faction of Republicans would join a faction of Democrats.

Conservative coup plotters might think Democrats will be tempted to go along for the ride just to make mischief. But Boehner can make a better offer to Minority Leader Nancy Pelosi and her caucus:

Dump me, and the next speaker is 100 times worse for Democrats. Vote to keep me, and we'll cut a reasonable budget deal and get immigration reform done.

Maybe Pelosi would try to sweeten the pot if Boehner's back is against the wall, perhaps insisting on jobs funding or corporate tax increases. But any deal they struck would give the Democrats more than they are getting right now, and more than they would get under new House management. So Democrats would likely take that deal in a heartbeat. Boehner has a "Get Out Of Coup Free" card.

Furthermore, Boehner should welcome a final confrontation with the Republican revolutionary wannabes. He would be doing both himself and his party a great favor by both instigating and defeating a far-right coup.

In the short-run, despite the fury that would come from conservative radio microphones and Twitter feeds, a House that functions is better for Republican chances in 2014 than a House that causes a global economic meltdown. And if he does want to continue on as speaker, he first needs Republicans to keep the House.

Now, of course, Republicans could just bide their time and dump Boehner at the outset of the 114th Congress. The Republican Caucus nominates a candidate for speaker following the midterm elections. If Boehner retains power with the support of only a minority of his caucus this year, next year he would likely fail to win re-nomination. But Boehner may have already decided he's going to quit by then. Why not act boldly now, and go out with his place in history sealed as one the greatest speakers ever, instead of one of the worst?

Boehner does not want to be remembered as the speaker who couldn't keep the government open, caused a global depression, threw away control of the House, and gave President Obama an extra two years to pass a wide array of liberal legislation.

He would prefer being remembered as one of the most consequential speakers in American history who saved the country from economic calamity, saved millions of immigrants from a life in the shadows, and saved his party from demographic doom.