House Republicans may have stumbled upon on a new plan to end the fiscal stalemate: Vote, and then run away.

Speaker John Boehner (Ohio), Majority Leader Eric Cantor (Va.), and Majority Whip Kevin McCarthy (Calif.) are considering holding a vote on a last-minute debt ceiling bill, and then, if it passes, leaving Washington, D.C. With under two days to go before the deadline to raise the nation's borrowing limit, the plan is designed to force Senate Democrats and President Obama to either accept the House's final offer, or trigger a default.

Rep. John Fleming (R-La.) explained the logic in more detail to reporters Tuesday afternoon.

"We want to make a deal that they can't refuse, and we're running out of time," Fleming said after a two-hour GOP conference meeting Tuesday morning. "Timing is very important here. They're going to be more motivated to take this up. Otherwise, they miss the Thursday deadline." [Talking Points Memo]

There is no guarantee the House will go through with such an extreme tactic — nor is there any sign the House can even craft a debt ceiling bill that could win the support of the Tea Party.

The Senate in late September approved a clean budget bill that would have averted the government shutdown. With the ball in Boehner's court, House Republicans left D.C. for the weekend right before the fiscal deadline. Yet that was more about giving the House time to respond, and lawmakers remained on call in case of a last-minute deal.

With the shutdown now in its second week, the Senate appeared to be on the verge Monday night of reaching a bipartisan agreement to raise the debt ceiling and end the shutdown. But outraged conservative House members pressed Boehner and company to draft their own plan to preempt their Republican colleagues in the Senate — a plan which reportedly went down in flames Tuesday morning for lack of support before Boehner could even publicly unveil it.

Needing to win more support, the House GOP is now racing to find a new solution. Boehner has said he would like to hold a vote Tuesday night, on a bill that will likely include more Republican demands.

Which brings us back to where we've been all along. If the House moves right on its next offer to appease the Tea Party, Democrats will likely balk, threatening a debt ceiling breach. Boehner could cut the Tea Party loose and strike a moderate deal with Democrats, but he'd risk his job and badly fracture his own party.

But it should go without saying that if the GOP goes through with the make-like-and-tree-and-leave strategy, it would surely destroy whatever credibility the party has left.

Update: ThinkProgress' Ian Millhiser explains the legal obstacles to the GOP skipping town, noting that Article II of the Constitution allows the president to "on extraordinary occasions, convene both Houses, or either of them." So if Boehner and company vote and immediately adjourn the House, Obama could, in theory, demand they come right back to work.

A tiny sliver of House members can also force the full House to meet:

Of course, House Republicans are nothing if not prone to defy this President, but the House rules account for the very circumstance where lawmakers try to prevent the lower house of Congress from operating by refusing to show up to work. Under those rules, "[i]n the absence of a quorum, a majority comprising at least 15 Members . . . may compel the attendance of absent members." Once such a vote takes place, the House Sergeant-at-Arms may send officers "to arrest those Members for whom no sufficient excuse is made and shall secure and retain their attendance." So if House Republicans try to flee town, they can be kept at work by force of law. [Think Progress]

That said, the debt ceiling deadline is almost here. All the procedural hurdles necessary to drag lawmakers back to work in time could render the entire process moot.