The failed budget negotiations may not be the end of the matter, however, because two scenarios could bring the parties back to the table. In the first place, the prospect of an additional $600 billion in defense cuts dismays many Republicans and not a few Democrats, including Obama’s outspoken Secretary of Defense. But the majority of congressional Democrats prefer sequestration to the alternatives, and Obama has strongly suggested that he won’t go along with the unraveling of automatic cuts. If the president is prepared to hang tough, in other words, he may spark a conflict between pro-defense and anti-tax Republicans. (Making matters even more interesting, many Republicans are both.) By using the defense cuts trigger as leverage, the president might be able to force budget negotiations involving a different, more flexible group of participants.

There’s also another, grimmer route back to the bargaining table, of course: The market could force the hands of the politicians. The events of the past six months have further weakened international confidence in U.S. governing institutions. Political risk analysis is something Americans used to do about foreign countries; now it’s something foreign analysts do about ours. It’s not hard to imagine a sequence of downgrades and shifts by foreign investors away from the dollar that could make continued partisan gridlock appear increasingly unaffordable. To be sure, some Republicans might hold out in the belief that a collapsing economy would assure victory in November. But that’s risky and would prove counterproductive if persuadable voters came to believe that Republicans were rooting for economic failure.

So in the face of all this, what should Obama do? He will be tempted to put the fiscal debate in neutral and run his 2012 campaign against Republican obstructionism. No doubt his political advisors will be telling him to preserve bright lines and sharp contrasts between himself and his Republican opponent in key areas such as Social Security, Medicare, Medicaid, and taxes.

This is the default position, and it could help Obama narrowly prevail next November. But the president should ask himself what a victory gained on this basis would be worth: What would he be able to accomplish in a second term? After all, his first term has shown that neither political party can impose its will on the other. Unless he were to win a victory as large as FDR in 1936 or LBJ in 1964 (and there’s no prospect of that), his second-term choices reduce to two: continuing gridlock or a new formula for doing the people’s business across party lines.