YOUR POLITICAL rival has miscalculated and left town with his tail tucked between his legs. What do you do?

The normal Washington response: exult while pretending not to, tut-tut at your rival’s irresponsibility and press your advantage as much as you can.

What if President Obama chose a different way? Having beaten the Republicans in the election and thrashed them in the post-election, what if he were to use his political advantage to serve the national interest? What might that look like?

The politics-as-usual route probably entails Mr. Obama working with Senate Democrats to pass a fiscal plan in the upper chamber that Republicans in the House can’t swallow, heavy on tax increases and light on spending cuts. If the House grumpily acquiesces, fine; if not, then Republicans can be blamed when the nation falls off the fiscal cliff.

But if he wants to resist the temptation of winner-take-all politics, the president could instead improve on the template for compromise that he and House Speaker John A. Boehner (R-Ohio) had been fashioning, before Mr. Boehner left the table for his ill-advised and ill-fated Plan B gambit. The speaker had given substantial ground, agreeing that revenue needed to rise and that higher tax rates for the wealthy had to be a component of that increase.

Mr. Obama, in turn, had offered substantial concessions of his own, agreeing to change the way cost-of-living increases are considered for Social Security and other benefits and offering to raise tax rates on households earning $400,000 and up, instead of his preferred $250,000.

That was the basis for a good agreement — not big enough, as we’ve said, but a significant start. Mr. Obama could improve on it, unilaterally. Defer to Republican objections to counting interest savings as spending cuts, for example, and plug the gap with additional genuine restraint on the growth of entitlement programs. At the same time, structure the changes to protect the most vulnerable recipients of federal aid. Then insist that Congress pass this truly balanced program and keep the nation from plunging back into recession.

What would Mr. Obama gain from such largeness of spirit? First, he would put the nation on a sounder fiscal path. As he understands, rising health-care costs and the aging of the population mean the nation can’t solve its debt problem through tax hikes alone. Controlling entitlements is a national necessity, not a partisan goal. Mr. Obama could remind his party that, as the creator of Social Security and Medicare, it has the larger stake in restructuring them to survive over the long term.

Paradoxically, Mr. Obama might also gain politically. He could embark on his second term with the freedom to think about immigration reform and gun control. He would enhance his stature as a national leader, bigger than party.

In his first public statement since Mr. Boehner’s Thursday night humiliation in the House, Mr. Obama merely reiterated his long-standing call for Congress to extend tax cuts on all but the top 2 percent. It’s not clear that the request stands any better chance now than before, and it is certain that, even if adopted, it would do nothing to solve the nation’s deep fiscal problem.

“Never negotiate with yourself” is usually a pretty good rule in politics. But Mr. Obama has no one left to negotiate with. In victory, he could seek a win for the whole country.