The nuclear reduction plan has been debated inside the administration for two years, and the options have been on Mr. Obama’s desk for months. But the document was left untouched through the presidential election. The president wanted to avoid making the reductions a campaign issue with Mitt Romney, who declared at one point that Russia was now America’s “No. 1 geostrategic foe,” a comment that Mr. Obama later mocked as an indication that Mr. Romney had failed to move beyond the cold war.

Mr. Romney, in turn, leapt on a remark that Mr. Obama intended to make privately to Russia’s then president, Dmitri A. Medvedev. He was picked up by an open microphone telling Mr. Medvedev that “after my election I have more flexibility” on missile defense, which Republicans said was evidence that he was preparing to trade away elements of the arsenal.

Among the most outspoken advocates of a deep cut has been a former vice chairman of the Joint Chiefs of Staff, Gen. James E. Cartwright, whom Mr. Obama continues to turn to on strategic issues. General Cartwright has argued that a reduction to 900 warheads would still guarantee American safety, even if only half of them were deployed at any one time.

“The world has changed, but the current arsenal carries the baggage of the cold war,” General Cartwright said last year. The challenges of North Korea, which is preparing a third nuclear test, and the possibility that Iran will get the bomb pose very different kinds of threats to the United States, and do not require the ability to deliver the kind of huge first strike that was the underlying logic of a large arsenal to face off against the Soviet Union.

“What is it we’re really trying to deter?” General Cartwright asked. “Our current arsenal does not address the threats of the 21st century.”

It is unclear how much money would be saved by the nuclear reduction plan that Mr. Obama is about to endorse; partly that depends on how the cuts are spread among the three elements of America’s nuclear “triad”: land-based missiles in silos, missiles aboard hard-to-find nuclear submarines, and nuclear bombers.

“These cuts don’t require a radical change in the triad, and that makes it politically easier,” said Daryl Kimball, the executive director of the Arms Control Association, which has argued for deep cuts. General Cartwright’s more radical plans, by some estimates, would have saved at least $120 billion over the next two decades.