The broad debate over President Trump’s fitness for the difficult and demanding office he holds has recently been reframed in a more pointed and urgent way: Does he understand, and can he responsibly manage, the most destructive nuclear arsenal on earth?

The question arises for several reasons. He has threatened to “totally destroy” North Korea. He has reportedly pressed for a massive buildup in the American nuclear arsenal, which already contains too many — 4,000 — warheads. And soon he will decide whether to sustain or set a course to possibly unravel the immensely important Iran nuclear deal.

Doubts about his competency were reinforced this week by Senator Bob Corker, who charged that Mr. Trump was treating his office like “a reality show” with reckless threats that could set the nation “on the path to World War III.” Mr. Corker, a Republican from Tennessee, says he is relying on Secretary of State Rex Tillerson, Defense Secretary Jim Mattis and John Kelly, the White House chief of staff, to help “separate our country from chaos.” That is a searing indictment, and Mr. Corker is no garden-variety legislator; as chairman of the Senate Foreign Relations Committee, he is a respected, and largely responsible, voice on national security issues.

Further, NBC News now reports that Mr. Tillerson judged Mr. Trump a “moron” after a July 20 meeting in which Mr. Trump, apparently distressed that the arsenal has declined since the Cold War, said he wanted a nearly tenfold increase in weapons.