In fact, governors have been complaining that they do not have nearly enough tests to give them the kind of information they need to make difficult decisions about reopening. They say they are competing with one another — and other countries — for the components that make up the testing kits, including nasal swabs and chemicals that detect whether the virus is present in a specimen.

Rather than one coordinated federal response, the Trump administration has been engaging on an ad hoc basis as states take the lead. In Kansas, for example, after an outbreak of the coronavirus in the meatpacking industry threatened to shutter plants that supply one-quarter of the nation’s meat, tests were ferried in by Kansas National Guard pilots in Blackhawk helicopters — but only after Gov. Laura Kelly, a Democrat, pleaded with Mr. Trump for help.

The Trump administration has come under intense criticism for not doing more, and for not providing specific guidance to the states about how much testing is necessary in its initial plan for reopening the economy, “Guidelines for Reopening America Again,” released this month. Outside experts have recommended that anywhere from 0.9 percent to 50 percent of the American public must be tested for the coronavirus every week.

“I think it’s really important that the White House has put out much more specific guidance for states around testing,” said Jen Kates, a senior vice president and director of global health and H.I.V. policy for the Kaiser Family Foundation, who has analyzed states’ capacity for testing. But the plan to test 2 percent, she said, “may not be enough.”