This post is part of Polyarchy , an independent blog produced by the political reform program at New America , a Washington think tank devoted to developing new ideas and new voices.

Kevin McCarthy is out as House speaker before he ever had a chance to even be elected speaker. Facing a serious challenge from the 40 or so hard-line conservatives and their unspecified and impossible demands, he has now acknowledged that he is not the person to unify the Republican Party. At this point, it's not clear who can. The party is deeply, deeply divided.

But if not the party, perhaps somebody could unify the House. So here's a crazy idea: What if a minority of Republicans who care about governing cut a deal with Nancy Pelosi and the Democrats to elect the next speaker of the House? Perhaps some mix of agreement on spending levels, plus bringing immigration and infrastructure to the floor? Maybe even a moderate Dem like Steny Hoyer could serve as majority leader?

There is still a small group of 50 or so Republicans, known as the Tuesday Group, who consider themselves to be center-right. The group is co-chaired by Adam Kinzinger (R-IL) and Charlie Dent (R-PA). Dent said in a recent interview, "We're the governing wing of the party and we want to make sure the leaders have an affirmative sense of governance." If Dent or Kinzinger (or someone else — Michigan's Fred Upton is another prominent) could lead even 30 of these center-right Republicans, they could join with Democrats to control 218 votes — enough to elect a speaker. From there, they could control key committee assignments.

How would this work? This group would not win a majority in the caucus vote. But they could vote strategically to support another Republican to bring things to a floor vote, and then defect when the entire House votes to elect the next speaker, as it must.

Sure, it's crazy. But so is the current impasse. A crazy situation may demand a crazy solution.

But in some ways, it's not so crazy. For most of the 20th century, Democrats controlled the House, but they did so with a mix of liberals and conservatives. It was only in the 1994 election, when Republicans took back the House, that many seats that had previously been held by conservative Democrats shifted to conservative Republican control, where they've mostly remained, except for a brief 2007-'10 interlude during which Blue Dog Democrats made a resurgence while Republican voters stayed home depressed.

So a coalition of liberals and moderates have almost always governed the House. And almost all the tough votes to keep the government running under Boehner's speakership have involved this coalition. Maybe it's time to just formalize it?

Democrats should take a deal because they know they're not going to control the House until at least 2021, given the current electoral map. They ought to be willing to bargain. After all, back in March, some Democrats said they'd support Boehner if he faced a coup attempt. As Rep. Jim McGovern (D-MA) said at the time, "Personally, I don't want to waste two years. And I think that the crazy Tea Party type would probably not be willing to work with us on anything."

By contrast, the far-right wing of the Republican Party has shown time and again it has no interest in bargaining. For them, compromise is anathema. They believe that through sheer force of will, they can somehow bulldoze the Senate and the president into massive government cuts and many other radical policies as long as they keep refusing a compromise. In the game of chicken they're playing, they have thrown out the steering wheel to prove they are so crazy that the other side has to swerve.

Wouldn't it be ironic, then, if their unwillingness to cut a deal would up empowering the remaining quasi-moderates left in the Republican Party, and forming a stable compromise majority that marginalized them once and for all?

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