The current budget standoff offers House Speaker John Boehner (R-Ohio) a historic opportunity: to become the first-ever bipartisan speaker, by striking a pact with House Democrats to switch his governing tactics as long as they support his right to lead the House.

It won't happen, of course. But it's worth exploring because such a dramatic move would address some of the problems bedeviling the nation's leaders right now, and just might change Congress' current trajectory.

Boehner--a fiscal conservative who made his mark on Capitol Hill by targeting the ossified Democratic majority's questionable tactics as part of the Gang of Eight -- has spent almost three years fighting both Obama and the tea party wing of the GOP. White House officials think Boehner is a mainstream Republican who would strike a deal on a range of issues but is terrified of losing his speakership to the far right of his party. Tea party members, meanwhile, have been pressing him to prove his conservative bona fides, and some of them even tried to remove him from power earlier this year.

And the press tends to trumpet two unflattering themes: that Boehner can neither manage his own conference nor make a credible deal with the White House. As a result, the narrative runs, Americans are left careening from fiscal crisis to fiscal crisis, and Congress can't even tackle popular initiatives such as immigration reform. A host of other potential changes supported by huge swaths of both parties -- from tax and entitlement reform to infrastructure spending -- are also left on the table just because of the fallout Boehner faces from a few dozen, ultra-conservative Republicans.

At least that's the rap against Boehner, whose speakership so far has been defined by blocking Obama's priorities rather than producing significant laws. But that could all change if he were just to decide to say to House Minority Leader Nancy Pelosi (D-Calif.): "Let's enter a grand coalition. Democrats will vote for me for speaker as long as Republicans hold a majority. And we'll do a budget deal that raises a little bit of tax revenue and reforms entitlements. We'll overhaul the tax code for individuals and businesses. We'll pass immigration reform and support the infrastructure spending that the U.S. Chamber of Commerce and labor unions want."

And, he can add: "We'll do it before 2014."

Conservatives would rebel and call him a traitor, but the press would go wild. His narrative will go from weakest speaker to one of America's best leaders. They'll rename the Capitol Dome the "Boehner Dome." The press will claim he's found a way to save the Republican Party.

Okay, let's get back to reality. Why won't this happen? For starters, it would be hard to imagine Democrats agreeing to vote for Boehner as speaker. And several Republicans who knew Boehner said they couldn’t envision him ever forging a deal with Pelosi. Robert S. Walker, who served in the House with Boehner in the 1990s, said he could try to address conservatives’ concerns by offering them a straight up-and-down vote on their proposals.

“He could just say to them, ‘All of you have great ideas, put them into an amendment, and you can offer it. We’re going to have an open amendment process, an open rule and the House can work its will,’” said Walker, who now serves as executive chairman of Wexler & Walker Public Policy Associates.

That approach, Walker said, would be less risky than forging a pact with Democratic leaders.

“What would really destroy him would be to cut a deal to allow the liberals to win,” he said.

But going by the numbers, Boehner could do it. While such a pact would likely prompt Republicans to convene a special conference to elect a new leader—that move requires a petition signed by 50 members. While that's a pretty steep hurdle, it's possible Republicans would be outraged enough to sign.

But once the issue reaches the floor for a vote, lawmakers can vote for anyone they’d like, which could help Boehner if he faced a massive defection within his own ranks. Former Rep. Jim Leach (R-Iowa) once voted for former Minority Leader Bob Michel (R-Ill.) instead of supporting then-Speaker Newt Gingrich, even though Michel had long left public service; former Rep. Gene Taylor (D-Miss.) made a habit of voting for then-Rep. John P. Murtha (D-Penn.) rather than the minority leader at the time, Richard Gephardt (D-Mo.). And a dozen House Republicans voted against Boehner as speaker during January’s floor vote.

So if enough of the 200 sitting Democrats joined with a sufficient number of the 232 sitting Republicans to cast 217 votes in Boehner’s favor, he would remain in office.

John Feehery, who served as then-House Speaker J. Dennis Hastert’s (R-Ill.) press secretary, described such a scenario in an e-mail as “pretty far-fetched.”

“Could something like this happen?” wrote Feehery, who is now president of QGA Communications. “Sure if the GOP split in two, but I don't think that will happen.”

Or, as Boehner spokesman Brendan Buck reacted to the idea in an e-mail, "This is so asinine the Washington Post should be embarrassed it wasted anyone's time with it."

Walker, who used to complain when the Democratic majority stifled the House GOP’s ability to express its views through voting, said House Republican leaders are doing the same thing.

“We have closed off the opportunity for the opposition to let their voices be heard. We’ve abandoned regular order,” he said. Boehner, Walker added, “is now a complete tool of whatever is the majority of the conference, rather than the whole House.”