WITH THE federal government less than six weeks away from hitting its legal limit of $16.4 trillion of debt, the fiscal-policy gap between President Obama and his Republican opponents in Congress seems unbridgeable. The GOP rejects additional revenue increases on top of the $600 billion Congress accepted to avoid the “fiscal cliff.” And Republicans insist they will not raise the debt ceiling without spending cuts to match. The president, for his part, likens this demand to hostage-taking and refuses even to consider any trade of debt reduction for a debt-ceiling increase.

Ominously, this partisan quarrel reflects differing perceptions of what would happen if the government did, indeed, lose the ability to borrow fresh cash. Some in the GOP insist that the Treasury could continue to make interest payments and meet other high-priority obligations out of current tax revenue, with no significant consequences for the U.S. credit rating or the economy. President Obama argues, correctly, that this is a reckless supposition.

Can, or will, Mr. Obama do anything to help the cooler heads within the Republican Party prevail? Or does he regard the debt-ceiling threat as a no-lose proposition for him and his party: either a GOP bluff or a promise to commit political suicide? Certainly Mr. Obama’s refusal to negotiate — coupled with his appropriate refusal to raise the debt ceiling through executive action — suggests that he’s willing to ride with the GOP right up to the brink.

However, the approaching debt ceiling is not the only inflection point facing the government and, possibly, the economy. On March 1, some $109 billion in automatic spending cuts kick in, the first installment of a “sequester,” evenly divided between defense and domestic programs, that is worth about $1 trillion over the next decade. On March 27, the most recent extension of federal spending authority will lapse, forcing a partial shutdown of government operations.

Though fraught with potential pain for the economy, and with potential political blame for the Republicans, neither the sequester nor a partial government shutdown poses quite the same risk, for the country or the GOP, that the debt ceiling does. Hence, the party retains some leverage. While Mr. Obama may refuse to negotiate over the debt ceiling, it’s not so clear that he and his fellow Democrats can avoid negotiating with the Republicans entirely — the urgings of certain members of Mr. Obama’s party to the contrary notwithstanding.

Fortunately, Mr. Obama left the door open to that possibility in his otherwise combative news conference Monday. Alluding to his close-but-no-cigar debt-reduction talks with House Speaker John A. Boehner (R-Ohio) after the November election, he suggested that there could still be a modified version of that near-deal, worth about $1.5 trillion over 10 years, including revenue raised by tax reform and “some additional cuts, including . . . reducing our health-care spending.” That would be unsatisfactory, relative to the country’s debt problem. But relative to the country’s current political and fiscal impasse, such an outcome would rate as a very happy ending indeed.