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I think at this point they're just not going to be able to elect anyone as House Speaker. All the most "popular" choices have been tried at this point, they're just cycling through the dregs now.

What happens next for the US government is a big shrug and a "who knows?" Their system of government was structured on the assumption that there would be at least some intention by the majority of its members to actually govern in a functional manner.

The extremist maga wing will never, ever cave. So it's up to the not-so-extreme Republican members to decide between A) cave to the extreme magas and elect one of them as Speaker, or B) negotiate with Democrats to form a coalition that can pass bipartisan legislation, leaving the extremists powerless, and elect a more mainstream (if you can still call them that) republican as Speaker. But working with Democrats in any way is poison to Republicans, who are terrified of getting on the wrong side of their "base" and the right-wing media, which would make them subject to death threats and violence to them or their families (yes this is a real thing).

Picture the "sweaty guy trying to decide between two buttons" meme and you see their dilemma.