With Majority Leader Kevin McCarthy dropping his bid for speaker, Paul Ryan ruling himself out of contention as well, and no other plausible contender emerging, the House of Representatives isn't in great shape at the moment. It's unclear if the body will get its act together in time to raise the debt limit and avoid government default. Republican members are reportedly breaking down in tears in the GOP cloakroom from all the stress. It's pretty bad.

Desperate times have a tendency to make ridiculous proposals seem reasonable, and so naturally some people — notably moderate Rep. Charlie Dent (R-PA) — are floating the idea that a speaker might be elected with Democratic votes:

Rep. Charlie Dent (R) says there may have to be a bipartisan coalition on the floor to elect the next speaker. — Sahil Kapur (@sahilkapur) October 8, 2015

This isn't unheard of at a state level. California Assembly Speaker (and later San Francisco Mayor) Willie Brown convinced a handful of Republicans to cross over and back him in the mid-'90s. The New York State Senate is currently run by Republicans with the cooperation of the Independent Democratic Conference, a small coalition of Democrats who favored continued GOP control of the chamber; while the Republicans would have a majority without them, they didn't before the 2014 elections, and still controlled the chamber.

But political scientists who study the House say it's unlikely, to say the least. For it to work, a group of Republicans must decide their interests are more closely aligned with Nancy Pelosi than they are with other Republicans. And the fact of the matter is that even the most moderate Republican is closer to other Republicans than she is to any Democrat. "No matter how fractured the conference is," George Washington University's Sarah Binder explains, "the differences within the party pale compared to the preferences between the two parties."

The parties are pretty well polarized

It's not exactly a secret that the Republican Party has moved considerably to the right — and the Democratic Party has more or less stayed where it is — since about 1980 or so. This chart from political scientists Keith Poole and Howard Rosenthal makes the point well:

As a consequence, the two parties are about as far apart as they've ever been in the history of the post-Civil War Republicaan/Democrat party system. The system that political scientists use to measure partisan ideology — DW-NOMINATE — is not without its flaws, but it's nonetheless a decent shorthand. Each member gets two scores: The first dimension measures how economically left-wing or right-wing a member is, and the second dimension measures the member's views on regional/racial questions (this dimension has largely stopped being useful post-1980 or so).

Here's how Poole and Rosenthal plot the current House, as analyzed in the context of its recent vote on funding the government. The x-axis is the first, left vs. right metric; the y-axis is the less important secondary metric:

That clump on the left is every Democrat in the House. The clump on the right is every Republican. That space in between them is the reason a bipartisan speaker probably won't happen.

Polarization makes a bipartisan speakership untenable

There are two forms a bipartisan speakership could take, both of which are probably ruled out by the polarization illustrated above. Option one: a plurality of Republicans (say, 180) try to convince a substantial number of House Democrats (38, in the 180 Republicans example) to back a Republican for speaker. Why would any House Democrat want to do that? Ideologically, even the most conservative House Democrat is closer to other Democrats than he is to an average, or even a more-moderate-than-average Republican. Effecting a Republican speakership isn't likely to give them anything they want policy-wise, at least not unless the Republican majority offers major, major concessions. It'd also risk losing them Democratic donors and the support of the national party.

And those concessions just wouldn't be credible. After years of House Republican leaders proving again and again that they can't control their membership, why should Democrats trust them to deliver the votes on, say, immigration reform, or some other measure they demand in exchange for supporting a Republican speaker? "We're already in that situation where Republicans can't deliver on those promises," Binder notes.

There also just aren't that many moderate Democrats left. "The Blue Dog Caucus is pretty small right now," Catholic University's Matthew Green, author of The Speaker of the House: A Study of Leadership, says. "Keep in mind that Pelosi has done a good job keeping those folks loyal to her. For them to decide to defect would be a pretty big deal. They're not nearly as unhappy with their leadership as the [right-wing Republican] Freedom Caucus is unhappy with their leadership."

Why would Nancy Pelosi want to be a powerless speaker?

Conceivably, the Democratic caucus as a whole could agree to such a deal. Nancy Pelosi could give 40-odd Democrats permission to go and caucus with Republicans, without negative ramifications. But it's not clear why she would. For one thing, she couldn't extract credible concessions. More importantly, though, why should she order 40 Democrats to the Republicans when she could demand that Republicans join with her 188 Democrats and make her speaker?

That's option two: All 188 House Democrats, plus 30 Republicans, elect a Democrat as speaker. But that doesn't make any sense either. Even moderate Republicans are closer to the Kevin McCarthys and Paul Ryans of the world than they are to Nancy Pelosi. "It's hard to imagine a sizable number of Republicans would want to throw their votes to the Democrats," Binder says. "It wouldn't be one of the remaining moderate Democrats — there aren't any conservative Democrats left — it'd be Nancy Pelosi."

My colleague Lee Drutman is more optimistic that this could happen, that there are 30 to 50 Republicans serious enough about governance to support a San Franciscan who backs single-payer health care as speaker. I'll believe it when I see it. The DW-NOMINATE data suggests even the moderate "Tuesday Group" is closer to the right-wing Republican Freedom Caucus, which forced Kevin McCarthy out of the race, than it is to Pelosi.

"This is truly a different world than anything we’ve seen, at least since the Civil War"

Maybe they care about stable governance enough that they think Speaker Pelosi — with Senate Majority Leader Mitch McConnell to temper her — is preferable to electing a speaker with the Freedom Caucus's support. But they'd have to be willing to do it and get nothing in return. Nancy Pelosi loses literally nothing by turning down that deal: if it falls through, she's still in the same place she started.

And even if she gets to be speaker, most of her initiatives would fail in the Senate, leaving her little incentive to give major concessions to Republicans in exchange for the ability to control the flow of legislation. Hell, they'd probably fail in the House as the same Republicans who voted for her speakership vote against them. Why would Pelosi want that kind of a rump speakership?

The speakership is, to quote Green, who literally wrote the book on the position, "a truly horrible job." Pelosi would be completely rational in rejecting a deal to retake it in these circumstances.

Then again, maybe everybody's wrong

A bipartisan speakership is the kind of idea the press loves. It reeks of statesmanship, compromise, and leadership. But it doesn't really serve the interests of anyone involved.

Then again, the situation is changing so quickly that making predictions based on precedent could be foolhardy. "None of us saw Boehner stepping away from the speakership," University of Virginia political scientist Jeffrey Jenkins says. "And none of us saw McCarthy recusing himself today. We seem to be in unchartered territory. A couple of weeks ago, I would have dismissed any thought of such a bipartisan coalition as implausible. I still don’t think it’s likely — but much more plausible, that’s for sure."

"Nobody knows what’s going to happen," Jenkins continues, "even ostensible 'experts' on speakership elections like me. This is truly a different world than anything we’ve seen, at least since the Civil War."

Correction: This article formerly said that the New York Senate has a Democratic majority but is run by a Republican minority with some Democratic help; that was true until the 2014 elections, but the body now has a clear Republican majority.