Turmoil in the US House has provoked a remarkable variety of creative proposals, which I’ll list in descending order of likelihood. In reviewing this list, keep in mind that the Speaker is elected by the entire House and need not be a US representative. The links are to articles making the case for these various scenarios.

John Boehner: Whether he wants to or not, the current Speaker could stay on as the Speaker. He is the only person in the world who does not have to win an election; he would just announce that he is staying on. He might be prevailed upon to do so if the alternative is a disaster. Or–conceivably–this was the outcome he foresaw all along.

Paul Ryan: The Wisconsin Rep. has broad support across the GOP caucus, so they might decide to vote for him unanimously and make him the Speaker. The main obstacle seems to be that he is steadfastly against running.  (“Was the crown offered him thrice?” / “Ay, marry, was’t, and he put it by thrice, every / time gentler than other, and at every putting-by / mine honest neighbours shouted.” … But look what happened to Caesar.)

Reps. Daniel Webster (sic) or Jason Chaffetz. They are running. But they don’t seem to have enough support in the GOP caucus to win, unless the Republicans face a protracted struggle and decide they’d just better pick someone who is seeking the seat.

Mitt Romney: The House GOP could select him if they wanted to (and if he accepted). Ezra Klein notes that they almost all endorsed him for president, so maybe he could unify their caucus. And they would get a prominent, effective leader from Capitol Hill.

“Colin Powell”: I use this name as an example of someone who might fit the following profile: popular and respected, with at least some GOP credibility and yet appeal to some Democrats. In the latest US poll of most admired humans, Powell gets zero percent, but so does everyone except a small group of people who are either disqualified (Pope Francis, Vladimir Putin, the current POTUS) or politically unacceptable to the House (Bill Clinton, George W. Bush). In any case, the scenario is that the House GOP decides they can look good by picking a popular figure and they replace the defectors on their side by drawing in quite a few Democrats who feel they’d be better off under Speaker Powell than under a House GOP leader. In fact, this idea could come from the Democratic side. (Speaker Buffett?)

Nancy Pelosi: She could get all the Democrats to support her, and if 29 moderate Republicans decided to join them, she would be elected. But those moderate Republicans stand far from Pelosi on the issues and would pay a price politically for supporting a Democrat. Moreover, if she compromised too much to get the 29 Republican votes, she could lose some Democrats or just decide herself that it wasn’t worth the candle.

See also why can’t a centrist coalition form in the US House? (Sept. 2013)