House Republicans Wednesday morning confirmed they would hold a vote on a stopgap government funding bill that includes a provision to defund ObamaCare, keeping alive the threat of a government shutdown if Congress fails to reach a budget agreement by September 30. But make no mistake: The GOP leadership does not believe it can win this fight.

Tea Party Republicans have threatened to block a budget bill, called the continuing resolution, that funds the government unless ObamaCare is defeated. They effectively used the summer recess to organize a groundswell of support for the plan and hijacked the GOP's fall strategy.

Fearing the blowback that would ensue from ignoring that highly influential wing, House Speaker John Boehner (R-Ohio), who has had trouble corralling his caucus in the past, is now going along with the gamble despite his reservations.

So far, the reality of the GOP's situation has failed to sink in with Tea Party members. "We have a real chance of getting defund or delay of Obamacare," says Rep. Steve Scalise (R-La).

But Republicans control only one chamber of Congress. Senate Democrats will assuredly kill a continuing resolution that defunds ObamaCare, as would President Obama. In short, the resolution Boehner is promising to put forward is doomed to fail from the start.

"House Speaker John Boehner and Majority Leader Eric Cantor are playing the last cards in their hand," wrote Politico's Jake Sherman and John Bresnahan, "and they're most likely losers."

Though a bill defunding ObamaCare has no chance of passing, Boehner, in giving it a vote, can simultaneously accomplish two things: He can appease Tea Partiers, and prove the need to compromise with Democrats. If and when the bill fails, he can reach across the aisle, go back to his caucus, and strike a budget deal without a defunding provision.

"National Review might have forgotten about the 200-plus Democrats in the House, but John Boehner has not," wrote Salon's Brian Beutler.

Boehner has shown before that when push comes to shove, he's willing to negotiate, even if that means going against the wishes of his party's most conservative members. To avoid a shutdown in 2011, he agreed to an 11th hour deal with lesser spending cuts than conservatives wanted.

This time, Obama may have even more leverage.

The president on Wednesday accused the GOP of trying to "extort" him. And polls show that the public would overwhelmingly blame Republicans in the event of a shutdown — a CNN survey last week found that 51 percent of Americans would blame the GOP, while only 33 percent would blame Obama.

Rep. Paul Ryan (R-Wis.), the GOP's budget guru, is privately taking a stand against the defund attempt for that very reason.

"We have to stay on the right side of public opinion," Ryan reportedly said during a GOP conference Wednesday morning, according to National Review's Robert Costa. "Shutting down the government puts us on the wrong side."

The dynamic ultimately comes down to this: If Republicans want to fund the government, they will at some point have to pass a spending bill that leaves ObamaCare funding intact. Anything else will die a swift death in the Senate.

"This doesn't fundamentally change our plans and it just delays the day when House Republicans will have to pass (or at least help pass) a CR," an aide to Senate Democratic leadership told the Washington Post's Greg Sargent. "If they don't, they will shut down the government. It's that simple. All procedural roads in the Senate lead to a clean CR. There is no scenario in which we pass anything that defunds or delays Obamacare."

In other words, Boehner will have to give in at some point in the next two weeks. Triggering a politically masochistic shutdown with no upside before doing is nothing less than a crazy proposition.