“We have failed,” said Evans J. R. Revere, who spent his State Department career trying various diplomatic strategies to stop the North. “For two decades our policy has been to keep the North Koreans from developing nuclear weapons. It’s now clear there is no way they will give them up, no matter what sanctions we impose, no matter what we offer. So now what?”

It is an assessment some of Mr. Obama’s aides say they privately share, though for now the administration refuses to negotiate with the North until it first fulfills its oft-violated agreements to freeze its nuclear and missile programs. A recent effort inside the National Security Council to devise a new approach resulted in a flurry of papers and classified strategy sessions — and the conclusion that all the alternatives to the current course were worse.

“We’re stuck,” one participant in the review said.

The only place any real change is visible is in the military planning by South Korea and the United States, which maintains a shrunken force of 28,000 troops in the South. For the first time since the armistice in 1953, officials say, the contingency plan for a conflict with the North treats the nation as a nuclear-capable adversary, despite the administration’s official refusal to acknowledge it as a de facto nuclear state. (What appear to be North Korea’s preparations for a fourth nuclear test, perhaps in the coming days, seem intended to remove all doubt.)

The latest revision of OpPlan 5029, the war plan for the Korean Peninsula, assumes that if a conflict broke out, the North would be able to deliver a crude nuclear weapon, though perhaps by truck or ship. American intelligence officials do not believe the North is yet able to shrink a bomb to a size that could fit on one of its Nodong missiles, the key breakthrough it needs.

“He’s put new effort into his nuclear program, missiles, special operations forces and long-range artillery,” said Gen. Curtis M. Scaparrotti, who took over last fall as commander of United States Forces Korea and the United Nations Command here. “They are using more underground facilities. He’s gone to school on how we operate.”