This is something I honestly don't understand. How can the Tea Party Caucus hold so much power over Boehner? Aren't there only around 50 of them in the House?
I understand they could get rid of him as Speaker, but wouldn't that in all likelihood result in Pelosi retaking the job? Why would any of them want that?
Honestly, the internal politics of the GOP Caucus are beyond my power to discern. Getting rid of Boehner through a direct vote would require an affirmative vote of 217* House members, and so would appointing a new Speaker, so in terms of REGULAR ORDER, it's basically impossible to get rid of Boehner. But if the caucus has its own rules regarding acceptable Speaker behavior and can somehow get Boehner to "voluntarily" resign, obviously he'd be gone.
At that point we'd be back in Speaker vote territory. Since you need 217 votes for a Speaker, Pelosi can't ever win that vote unless some Republicans actually cross the aisle and vote for her. So it would be up to the GOP to find a candidate that could command 217 Republican votes. Given their previous success whipping for things like "don't shut down the government", it might take them a little while.
Also, as far as the Hastert Rule goes, how many Republicans in the House would actually pass a clean CR? If it's everyone except the tea party then wouldn't that fulfill the rule easily?
Two issues here -- the first is that, because of all the drama, Boehner adopted a super-Hastert Rule in his Speakership -- he only brings up bills that can command 218 Republican votes. The problem is that he used to have about 250 votes to play with -- now he has more like 230. That's a very tight margin of error.
The second issue is that there are actually three positions in the GOP caucus:
a) Will always vote no, wants to watch the world burn
b) Will vote yes on CR, rational actor
c) Will support passage of a clean CR
as long as they can vote against it
Group C is the one that makes this especially complicated, because in order to fulfill their wishes, Boehner has to bring up the bill against their expressed desires. As you can imagine, accomplishing that isn't straightforward.
* one is dead right now