“Our leaders in the federal government at every level ought to be thinking of this moment as December 8, 1941,” Mr. Inslee said, calling for “the same federal response we had the morning after Pearl Harbor.”

Mr. Hogan also said he was pleased that Mr. Trump seemed to be taking the virus more seriously, but suggested that it was overdue and he should have looked to the governors sooner. “His messaging sounds a lot more like the way I’ve been talking and some of my colleagues have been talking about it for weeks,” he said.

The political process, Mr. Hogan continued, “is broken and needed a shock to the system. He said that while “it’s terrible it took this, maybe when we all recover we really can end some of the divisiveness and dysfunction.”

Mr. Trump, of course, has benefited from and fostered divisiveness since he began running five years ago. And given his penchant for showmanship and impulsiveness, he could have a difficult time sustaining any attempt at restraint, as his attack on Ms. Whitmer shows.

He also refused to acknowledge his early and well-documented skepticism about the seriousness of the virus. “I’d rate it a 10,” Mr. Trump told reporters Monday when asked to grade his performance. And on Tuesday, Mr. Trump said, “I felt it was a pandemic long before it was called a pandemic,” contrary to weeks of his own statements.

But the bigger question coming out of this crisis may be whether the new premium on competence and experience can lessen the polarization that has come to define American politics in this era.

With many in government and business predicting a terrible human cost from the virus as well as a national economic catastrophe, the partisan appeals to ideology and tribalism are bound to lose some of their salience, at least in the short term.