I think this is a little bit of a far-fetched scenario, but it's worth noting that even if John Boehner gets behind this Senate deal and it passes this afternoon we might force the Treasury to run out of cash anyway.
The reason is that a lone Senator—Ted Cruz, say—can cause massive delays on the passage of a bill if he wants to. In practice, to move quickly the Senate needs "unanimous consent" and Cruz seems to be at least playing footsie with the idea of denying it. Everyone's level of certainty about this has to be pretty low, but I'm of the view that even if we were pushed slightly beyond the X-Date for reasons of legislative procedure that nothing disastrous would happen. A fair amount of damage has already been done to economic confidence, and the incremental amount of additional damage that Cruz could do with pure stalling tactics is (relatively) low. The real risk of stalling us over the deadline is precisely that it might not be so bad, which in a lot of ways would only inspire more brinksmanship down the road. America's become a bit like the proverbial frog in boiling water, where the cumulative damage of government-by-crisis is quite large but no one event is cataclysmic enough to break the cycle.