I should begin by clarifying terms. Perhaps the headline should read: "...save McCarthy's speakership," because I am not talking about whether Democrats will either step in to avert a government shutdown or eventually offer House Speaker Kevin McCarthy a path to ending such a shutdown, because at this point one of those is almost inevitable. There will eventually be a short-term deal, it will pass the House, and it will pass with mostly Democratic votes. The Senate will then pass it as well and President Joe Biden will sign it. I'm not talking about saving McCarthy from the shutdown nonsense (which may happen or not), instead I'm talking about what might happen afterwards... or even "during."

The radical (read: lunatic) fringe of the House Republicans -- let's call them the Chaos Caucus -- are going to be completely incensed by this eventual deal. Not the deal itself so much as the fact that Kevin McCarthy didn't have a magic wand or some fairy dust which would -- hey presto! -- make them the ultimate arbiters of the federal budget. It's pretty obvious that for some of the crazies the only acceptable answer is for them to magically gain the power to somehow jam their own budget down the throats of the Democratic Senate and a Democratic president. Which McCarthy simply cannot provide (because McCarthy, unlike them, must make occasional forays outward from Republican Fantasyland into actual reality).

If any one of the lunatics gets incensed enough, he or she can file a "motion to vacate the chair." This is a sort of no-confidence vote in the House. If a majority of those present vote for it, then McCarthy will no longer be speaker. Since the House will be speakerless, their only order of business at that point would be to try to elect a new speaker. Which could lead (remember January?) to endless votes that all fail to provide a majority to any candidate. This would grind Washington to an absolute halt, for the most part.

The timing of all this (if it happens) will be critical. The motion to vacate can be called for at any time. If the hotheads know full well that the House is on a path to actually solving the immediate budget crisis (by passing some sort of short-term compromise deal worked out with the Senate and White House), then they could move immediately to oust McCarthy. Or they could wait until after the bill makes it to Biden's desk -- which seems much more likely.

I say this not because I have any deep trust in the sanity of any of the GOP Chaos Caucus (I don't) but because a motion to vacate before the deal has passed would almost certainly fail. There aren't a whole lot of the hotheads -- maybe a couple of dozen, max. Even if you add in Republicans who are scared of the wrath of the MAGA base, they're never going to get a majority behind them for such a vote. There are reportedly on the order of 180 Republicans who will vote to support McCarthy, and they'd need almost all of them to suddenly decide not to.

You'll notice that I'm only counting Republican votes, however. I am assuming that all of the Democrats would not vote for a motion to vacate before the budget problem had been (even temporarily) solved. They'd want to see the deal go through (especially if the government has already shut down).

But afterwards? Well, that could be a different story.

There is no clear candidate to take McCarthy's place. For starters, nobody really wants the job, because it is an impossible one. McCarthy isn't the first Republican to find this out -- just ask John Boehner or Paul Ryan, they'll tell you the same story. The lunatic fringe simply cannot be placated, therefore nothing much ever gets accomplished. Which must be frustrating, for any speaker. So who would want such a headache? The crazies might support one of their own, but none of them will ever get the support of the full Republican caucus.

If Democrats are faced with a motion-to-vacate vote after a budget deal has passed, what would there be to stop them from all voting for it? That way, the handful of crazy GOP representatives who hate McCarthy would get their way -- with mostly Democratic votes. McCarthy would be deposed.

The political calculation for Democrats in such a situation would go something like this: either McCarthy continues as one of the weakest speakers ever, or the House absolutely grinds to a halt for a while. Republicans would be on the news every night fighting among themselves, in increasingly bitter terms. Their dysfunction would be on display for all to see. All Democrats would have to do is stand back and say: "See? This is the chaos that happens when you put Republicans in charge."

A House doing nothing other than waste time on endless speaker votes is a House that isn't doing anything worse, after all. That would be a big part of the political calculation for Democrats. All committees would stop all their hearings and whatnot. All investigations (including the impeachment inquiry) would halt. All of the day-to-day performative nonsense simply could not take place, since the House would be in constant session holding vote after vote after vote for speaker.

There would only be three possible outcomes of such chaos. Four, if you count "the House doesn't do anything until January of 2025" when a new Congress will convene, but that's a little too farfetched to contemplate. Assuming there is an eventual conclusion to the chaos means that someone will be elected speaker. The three possibilities (as I see them):

Kevin McCarthy -- if he's got something like 180 Republicans (or more) behind him, then he'll obviously be the strongest candidate for the job on the GOP side. He could repeat his performance from January and cut lots of secret deals with all the hotheads and get them to either vote for him or just vote "present," and he could eventually claw his way back into the speaker's chair.

Or this could happen a different way, too. McCarthy could cut some kind of deal with some Democrats to vote to allow him to be speaker (more on how this would happen in a moment). This would be shocking, but I could see it happen, if such a move was blessed by Hakeem Jeffries and the rest of the House Democratic leadership. What concessions could they wrest from McCarthy? Well, they couldn't be too radically partisan, since any such deal might mean McCarthy would start losing those 180 votes, but Democrats could indeed get some guardrails put up in exchange for saving McCarthy's political hide.

Some other establishment Republican -- Steve Scalise is the Republican most often mentioned as a possible successor to McCarthy, since he's already on the GOP leadership team and enough Republicans seem to have enough respect for him that he might be an acceptable choice. But the only way I can really see this happening is if McCarthy decides to give up and hand the reins over to someone else (most likely, in total disgust). Scalise would probably not directly challenge McCarthy without him bowing out, and McCarthy's supporters wouldn't switch their votes over unless they knew McCarthy was behind such a move.

Scalise (or whatever other acceptable Republican they wind up with) would have the same problems McCarthy faced, however. He'd likely have to make the same sorts of secret deals with the Chaos Caucus members, and his leadership would be just as hamstrung from the get-go. He'd have a different personality than McCarthy, but beyond that it's hard to see much fundamentally changing in the House Republicans' behavior at large.

Hakeem Jeffries -- Minority Leader Jeffries is the highest-ranking Democrat in the House and (as in January) all the Democrats will vote for him even knowing he's going to fall short of a majority. But with the Republican Party's razor-thin majority, Jeffries would indeed get close. And it wouldn't take all that many Republicans crossing the aisle to actually vote in a way that would allow Jeffries to actually win. Here's how it might work (this is the same scenario that McCarthy might use as well, just in the other direction):

Let's run the numbers (assuming there is a full House and everyone is present, just to make it easy). With 435 total members, a majority is 218 (since half of 435 is 217.5). Back in January (again to make the math easy), Jeffries received 212 votes each and every time the House voted. So let's say the first speaker vote after McCarthy has been ousted goes something like:

212 -- Hakeem Jeffries

208 -- Kevin McCarthy

15 -- (various other votes for people from the Chaos Caucus)

Nobody gets a majority, so nobody wins and another vote is called for. The easiest way for Jeffries to actually win would be for six Republicans to switch their vote from McCarthy to Jeffries, which would give him the 218 he needs. But there's another way, too. The majority is calculated as "the majority of the votes cast for an actual person." Voting "Present" means your vote is not counted when figuring what majority is necessary. McCarthy actually used this to his benefit, to secure his final vote when he became speaker. So what if Democrats convinced enough Republicans to sit the vote out? Here's what it would take:

212 -- Hakeem Jeffries

196 -- Kevin McCarthy

15 -- (various other votes for people from the Chaos Caucus)

12 -- "Present"

This would reduce the total number of votes cast for any one person to only 423. And half of 423 is 211.5. Meaning Hakeem Jeffries becomes the next speaker.

Of course, Democrats would have to make some promises in order for this to happen, because crossing the aisle in such dramatic fashion is not exactly going to be popular with the Republican base. But it is not entirely outside the realm of the possible.

Those are the three options I see: McCarthy, some other mainstream Republican, or (in a surprise move) Hakeem Jeffries. Since one of the first two is far more likely, it doesn't seem like much would change at all. Except that a large chunk of time would have been spent displaying to the American people how the Republican House caucus is no better than a roomful of cranky toddlers. Which wouldn't be such a bad thing, heading in to an election year where they'll all be up before the voters again.

The political media will, right up until it happens, be focused in on whether a motion to vacate the chair will ever happen or not. Little time will be spent (until it actually happens) speculating about the mechanics of it all. But the hard truth is that with something like 180 or more Republicans solidly behind Kevin McCarthy, his fate as a House speaker is going to rest with the Democrats. If they join the Chaos Caucus on the motion to vacate, McCarthy will be removed. And one of the only ways McCarthy might have to gain the gavel back would be for him to start cutting deals with Democrats, which would certainly change the dynamic in the House for the better. But either way, if the hotheads do attempt to remove McCarthy, his fate might ultimately be in Democratic hands.

-- Chris Weigant

Follow Chris on Twitter: @ChrisWeigant