For 13 months in the Oval Office, and in an unorthodox business career before that, President Trump has thrived on chaos, using it as an organizing principle and even a management tool. Now the costs of that chaos are becoming starkly clear in the demoralized staff and policy disarray of a wayward White House.

The dysfunction was on vivid display on Thursday in the president’s introduction of tariffs on steel and aluminum imports. The previous day, Mr. Trump’s chief economic adviser, Gary D. Cohn, warned the chief of staff, John F. Kelly, that he might resign if the president went ahead with the plan, according to people briefed on the discussion. Mr. Cohn, a former Goldman Sachs president, had lobbied fiercely against the measures.

His threat to leave came during a tumultuous week in which Mr. Trump suffered the departure of his closest aide, Hope Hicks, and the effective demotion of his senior adviser and son-in-law, Jared Kushner, who was stripped of his top-secret security clearance. Mr. Trump was forced to deny, through an aide, that he was about to fire his national security adviser, Lt. Gen. H. R. McMaster.