He faces a vote on his speakership on January 3rd, and he isn't going to be going into that vote a hero no matter what he does now. If he cuts a deal with the House Democrats and the administration, most of his caucus will be enraged, but if he doesn't get a deal done, he'll be seen as a totally ineffectual leader who doesn't have the trust of his own party. Ironically, the latter scenario gives him a better chance to keep his job.
To be fair, not all Boener's failures can be attributed to the man himself. A solid 20% of the Republican House is comprised of government-hating teabag lunatics who have no business on the Hill in the first place; they are #$%$ reactionaries on a par with crappygambler and that she-cracker from Texas. But the GOP has nobody to blame but themselves: they've been shoveling garbage down the throats of their base for decades, reinforced 24/7 by the opinings of Limbaugh and Faux News.
Boehner presided over the most ineffective Congress in history. This is the worst session. Nothing was accomplished, except the systematic downgrading of our creditworthiness by the Tea-Droolers and other anti-government lunatics.
I believe the worst was 2009-2010. Only 2 things passed was Obama care when people were crying out for jobs and the stimulus.. And Pelosi & Reid had a super majority. Lots of bills were sent to the senate and Reid/Obama pocket vetoed them. Be Fair!
Boehner's problem is that he's basically spineless.
As Speaker, his job is mainly administrative; one could argue the role of Speaker is comparable to that of office manager. Keep everyone in line and make sure the House is functioning properly, and to liaise with the President. I am guessing that Boehner has delegated many of his responsibilities to Eric Cantor (House Majority Leader)...
And Cantor is great at his job. He's a hard-right conservative and he's smart enough to avoid the limelight...possibly the closest thing to pure evil since Cheney. Or maybe more: Cheney was always a corrupt cynic, but Cantor is a true believer.
Think of it this way: Cheney was to W as Cantor is to Boehner. And since Cantor is only 49 he has nowhere to go but up. A run for the White House in 2016 isn't out of the question, although I think a 2020 run is more likely - at which point he'll still be under 60.