Ezra Klein has an interesting post this afternoon arguing that the president's decision to go public is a sign that there's no deal to be had on the deficit, and that there won't be until after the deadline is reached.
That may well be true. However, there's one important piece of the puzzle to always keep in mind: before the deadline or after, sooner or later the debt limit will go up. Which means that sooner or later, a majority of the House is going to vote to raise the debt ceiling. So will a majority of the Senate -- quite possibly, a filibuster-proof majority. And the Barack Obama is going to sign it.
Now, this may happen after the House votes down one or more attempts; it might happen after one or more presidential vetoes, or after one or more cloture votes fail. It may happen after the nation plunges into an economic panic, or after crazed Social Security (non-) recipients and government contractors storm the Capitol. Indeed, I agree that it's perhaps more likely than not that it will take something like that to push everyone over the line. But over that line, sooner or later, they'll get.
And everyone knows it. Everyone knows that sooner or later Barack Obama and John Boehner are going to sign off on something -- it takes a presidential signature, and there's no conceivable way to get to 218 votes in the House without Boehner, and as I've said the odds are good that it needs Eric Cantor, as well. Obama knows it. Boehner knows it.
I'm not sure how that will play out over the next several weeks. But any analysis of the players involved has to include that eventually, they are going to sign off on increasing the debt limit.