House Democrats fighting for leverage in the GOP Congress are hoping they can empower an unlikely ally: Speaker John Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE (R-Ohio).

Democrats are outnumbered by more than 50 members – and have almost no power to bring bills to the floor.

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But they see Boehner as a willing compromiser on must-pass legislation like funding the government and raising the debt ceiling – once the Speaker can convince his troops that the partisan route endorsed by his conservative wing has been denied.

By banding together in veto-sustaining majorities against conservative proposals demanded by Boehner’s right flank, Democrats hope to both sink those GOP measures and grease the skids for more moderate compromises.

“[The Republicans] have a majority party that's deeply divided,” Rep. Steny Hoyer Steny Hamilton HoyerHouse Democrats postpone vote on marijuana decriminalization bill Democrats scramble on COVID-19 relief amid division, Trump surprise The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (D-Md.), the Democratic whip, said Thursday from his office in the Capitol.

“And … what we've learned is if we stick together – and we have been sticking together, we've been very unified – that it can empower Speaker Boehner at some point in time to say, 'Look, I tried every which way I can think of to accomplish the objectives that our caucus wants to do. But if I can't accomplish those, I will not allow the government to shut down, the debt limit to be not extended, or other things that are harmful to the country,’” Hoyer said.

Those dynamics were on full display in the recent fight over funding for the Department of Homeland Security (DHS).

House conservatives had insisted that the package include amendments blocking President Obama's executive actions on immigration, and the House passed five such provisions on largely party-line votes.

Senate Democrats, however, blocked the package on four occasions, forcing Senate GOP leaders to pass a clean DHS bill and send it back to the House. With conservatives adamant that the immigration provisions be attached, Boehner tried to buy time with a three-week extension of the agency's funding – a measure that died in a surprise vote when all but 12 Democrats joined those conservatives in opposition.

With the deadline for a partial DHS shutdown fast-approaching, Boehner sat his conference down and explained why caving on immigration was the only way out.

“I am as outraged and frustrated as you at the lawless and unconstitutional actions of this president,” Boehner said just before bringing a long-term DHS funding bill – without the immigration language – to the floor. “I believe this decision – considering where we are – is the right one for this team, and the right one for this country."

The legislation passed 257 to 167, with only 74 Republicans joining Boehner in favor. All the Democrats voted 'yes.'

Democrats hailed Boehner's shift – and are hoping it offers a template for the tough debates to come.

“I think that's the appropriate attitude for him to take,” Hoyer said Thursday. “I hope he continues that.”

There are signs he intends to. After years of Congress's failure to enact a long-term solution to Medicare's perennial problem stabilizing physician payments, Boehner has teamed up this year with House Minority Leader Nancy Pelosi Nancy PelosiSunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election Trump is betting big on the suburbs, but his strategy is failing 'bigly' Trump orders flags at half-staff to honor 'trailblazer' Ginsburg MORE (D-Calif.) in search of a fix – an agreement that could arrive within days.

Boehner's decision to reach across the aisle carries no lack of political risk for the Speaker, who is already under fire from conservatives critical that he's not fighting hard enough against Obama's policy agenda. Indeed, 25 Republicans voted in January to strip his Speaker's gavel. And the resistance from the right has persisted since then, forcing GOP leaders to pull a number of their priorities from the floor even as they control the largest Republican majority since the Great Depression.

“I’m heartbroken,” conservative GOP Rep. David Schweikert said of Boehner's strategy in the DHS fight. “There were things we could have done to lay out our story, our argument and our options. … We failed to embrace that opportunity.”

Boehner has brushed off the criticisms, saying they're all part of the messy business of legislating in the “rambunctious” House. He's also offering no apologies for working with Pelosi on Medicare's “doc-fix.”

“There was an opportunity that presented itself to work in a bipartisan way to find the appropriate offsets, spending offsets,” he said Thursday. “The door opened, and I decided to walk in it. As simple as that.”

Pelosi, for her part, says she's “always had a good rapport” with Boehner, and appears only too happy to be working with the Speaker on a Medicare bill, even in the face of pushback from some liberals in her own caucus.

“I call it the giant kaleidoscope,” she said Thursday. “You never know when you turn that dial who's going to be part of the formula for passing a bill.

“We're always a resource to each other,” she added, referring to Boehner, “and hopefully, … this will be a good example of how we go forward.”

There will be plenty of opportunities to test the formula.

Aside from an April 1 deadline on the doc-fix, Congress must soon address funding for the Highway Trust Fund, which runs dry in May, and the future of the Import-Export bank, whose charter expires in June. And in the fall lawmakers will again be forced to pass the spending bills that keep the government running, as well as legislation to raise the debt ceiling.

Boehner has vowed there will be no more government shutdowns or threats of Treasury defaults on his watch – a message echoed by Senate Majority Leader Mitch McConnell (R-Ky.). And, encouraged by the DHS debate, Democrats seem ready to take the Speaker at his word.

“This is a guy who worked with Teddy Kennedy and George Miller in passing No Child Left Behind,” Hoyer said this week, referring to a landmark education reform law enacted in 2001. “This is not a guy who's been unwilling throughout his career to work across the aisle.”

There are limits, however, to the Democrats' cooperation with Boehner. GOP leaders, for instance, should not expect any Democratic help in passing their 2016 budget package, which limped through the committee process this week.

Pelosi said the Republicans' proposal will “take us back to the failed economic policies under President Bush,” while Hoyer said he expects “no Democrat” will back the package.

“They're going to have to find 218 of their folks,” he said.

The House is expected to vote on the budget bill next week.