Mr. Obama has long advocated a “nuclear-free world.” His lieutenants argue that modernizing existing weapons can produce a smaller and more reliable arsenal while making their use less likely because of the threat they can pose. The changes, they say, are improvements rather than wholesale redesigns, fulfilling the president’s pledge to make no new nuclear arms.

But critics, including a number of former Obama administration officials, look at the same set of facts and see a very different future. The explosive innards of the revitalized weapons may not be entirely new, they argue, but the smaller yields and better targeting can make the arms more tempting to use — even to use first, rather than in retaliation.

Gen. James E. Cartwright, a retired vice chairman of the Joint Chiefs of Staff who was among Mr. Obama’s most influential nuclear strategists, said he backed the upgrades because precise targeting allowed the United States to hold fewer weapons. But “what going smaller does,” he acknowledged, “is to make the weapon more thinkable.”