Boehner has no control over the far right wing of his caucus. They wouldn't provide him enough votes in the House to force through his own, "**** negotiating!" budget plan, because they didn't want to violate Grover Norquist's anti-tax pledge. Having realized that this has stripped him of all negotiating power (after all, if the highest-ranking Republican in the House can't get his caucus to vote for a budget plan designed by Republicans for Republicans, how can he be trusted to deliver Republican votes on a broader compromise bill?), he's passed the buck to the Senate. The problem with that is that the Senate can't originate omnibus budget legislation, since all revenue-related bills are Constitutionally required to originate in the House (Article I, Section 7, Paragraph 1).
If the Tea Party types don't back off on the Norquist pledge beforehand, then there will be no deal until the election for Speaker of the House is over. At that point, if he's still Speaker, Boehner can hash out a compromise with House Democrats and more moderate Republicans. If he's not still Speaker, then it's hard to say, as how long it will take to get a deal will depend entirely on who replaces him, and who will be the next Speaker of the House is a topic worthy of a thread unto itself.
Either way, we're not getting a deal, prior to the new year, when the sequester kicks in. I wouldn't expect it to last beyond January, though. Actually, I wouldn't expect it to last much beyond the first week of January. Boehner just needs to stonewall the Senate and President long enough to secure his next term as Speaker. The Speakership election is typically one of the first orders of business in the House, upon returning after an election year. The 113th Congress will convene on January third.
In fairness, if House Democrats wanted to speed a deal, they could pledge to support Boehner's ongoing Speakership, if he'd start negotiating with them in the room, alongside moderate House Republicans, while cutting the Tea Party caucus out entirely. That would reduce/eliminate his political need to be so obstinate in negotiations, prior to that particular vote, but House Democrats are probably individually worried about how poisonous supporting Boehner could be to their own careers, further down the road.
Coincidentally, the government shutdown of 1995/1996 lasted twenty-eight days. It ended on January sixth of 1996, three days after Congress reconvened and reelected Newt Gingrich as Speaker of the House. I say this, just in case anyone was looking for a bit of historical precedent regarding this kind of situation.
[addition]
So basically taxes are going to go back to what they were before the Bush cuts, right? That sounds awesome, is there some other part I'm missing?
Yes, in addition to the taxes returning to Clinton-era levels, spending will be slashed, by $1.2 trillion, with very few areas exempt from cuts. (Ex.: The normally untouchable Defense budget is subject to the wanton cuts, and while military officers cannot have their salaries reduced, they can be furloughed or fired, hence Scotty's justified unease.)
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