The deal, unfortunately, does include one minor health care provision that requires the administration to certify that procedures are in place to verify the incomes of those seeking insurance subsidies. (By the middle of next year, an inspector general will have to audit those procedures.) A White House official said the provision was virtually meaningless and would have no effect on the rollout of insurance exchanges, but the requirement was unnecessary and adds a tarnish to the president’s vow not to pay the slightest bit of ransom to Republicans.

Nonetheless, the outcome vindicates the strong stance taken by Mr. Obama and Senate Democrats against the Republicans’ extortionate demands. Two years ago, when he was first confronted with the Republican refusal to raise the debt ceiling, Mr. Obama blinked and agreed to a budget control law that severely slashed domestic spending and will continue to do so for years through the sequester.

Determined not to give in this time, he refused all of the most outrageous demands. The Republicans pushed the nation to the brink of default, and pulled back at the last minute when it was clear the White House would not capitulate.

But this doesn’t mean the brinkmanship is over. The continuing resolution that pays for the government to reopen lasts only until Jan. 15. Democrats won a formal budget negotiation that Republicans had resisted for months, giving them a chance to relieve some of the sequester cuts. Republicans have already vowed to use the budget negotiations to keep up their attacks on the health law. “Our drive to stop the train wreck that is the president’s health care law will continue,” Mr. Boehner said in his surrender statement.

Then, on Feb. 7, the Treasury will again hit the debt ceiling. That will be closer to the midterm political season, and the futility of trying to use default as a weapon should be a fresh memory for Republicans. But many in the party remain defiant, opposing this week’s deal and vowing to keep waging their crusade. Those who refused to submit to blackmail in Washington need to remain vigilant.