The roster of presidents who could not conquer crisis when it arrived is long and inglorious — James Buchanan, who failed to stop the South from seceding; Grover Cleveland, who failed to stem the Panic of 1893; Herbert Hoover, who failed to overcome the Great Depression; Jimmy Carter, who failed to end the Iranian hostage standoff until his last minutes in office.

But there are others who rose to the occasion, probably none more than Abraham Lincoln, who found his country falling apart when he took the oath and responded with calm determination and a willingness to work with rivals in a common cause. Roosevelt took office at the depths of the Depression and likewise projected confidence and took decisive action while still leveling with the American people about the scope of the challenge.

While Mr. Trump has tried to reassure the public, saying that the coronavirus was “under control” and would “go away,” he has not sounded to many ears as if he were fully acknowledging the scope of the problem.

Ms. Goodwin said Roosevelt demonstrated the way to balance messages in his inaugural address in 1933. While the speech is often remembered for his line that “the only thing we have to fear is fear itself,” he also made a point of telling Americans that “only a foolish optimist can deny the dark realities of the moment.”

“Instinctively, he is trying to stem the panic,” Ms. Goodwin said. “But what has to be connected to that is the recognition of the problem.”

When World War II threatened, Roosevelt invited Republicans into his cabinet to foster national unity. As the virus spread over the weekend, Mr. Trump declared that he would skip the annual bipartisan St. Patrick’s Day luncheon out of disdain for Speaker Nancy Pelosi, who led his impeachment and ripped up his State of the Union address.

Other presidents effectively took on dire if less daunting crises. Theodore Roosevelt marshaled the full resources of the government, including the Army and Navy, after the devastating San Francisco earthquake of 1906. Lyndon B. Johnson rushed to New Orleans immediately after Hurricane Betsy, visited a darkened shelter, illuminated his face with a flashlight and called out: “I am your president. I am here to make sure you have the help you need.”