The tea party went into this shutdown with no exit strategy (betraying the fact that most of them are politically inept). They used threats of primary challengers against moderate Republicans and threats against Boehner's position as speaker.
The poll numbers are damning, this thing is going to be laid at the Speakers feet. He is at least going to be challenged as Speaker, and possibly will be ultimately primaried if this ends in any way that keeps Obamacare intact, and does not give the Repubs something to claim as a victory.
Here's how we get the government back in business...
We promise Boehner full, unconditional support from the Democratic Caucus on any challenge to his position as Speaker of the House.
We know he is a weak man, we know that in the waning hour of the shutdown he passed a rule that made only him or a "designee" capable of bringing forward a CR to a vote. I think it's clear that his position as Speaker is in play, and that is why he is playing to the extremists of the Republican base. If we give him an out that covers his position as Speaker he will allow a vote on a clean CR.
Should this happen I doubt that he will be able to keep his seat, but frankly I don't see many scenarios that involve him keeping his seat anyway given the current circumstance. I hear K Street is pretty kind to former Speakers of the House.
Minority Leader Pelosi, Minority Whip Hoyer, offer Boehner a deal that covers him, and him alone and I bet we will finish this nonsense quickly.