New Jersey and New York state have borne the heaviest toll from the spread of the coronavirus, accounting for more than half of the nearly 21,000 deaths in the U.S. as of Sunday morning. Governors and local officials are on the front lines of mitigation efforts, imposing isolation and social-distancing orders far stricter than federal guidelines. They and health experts warn that without more reliable testing for possible immunity as part of any effort to reopen the economy, areas that have made hard-won progress against the disease could suffer a deadly setback.

“We’re fighting to stay ahead on bed capacity, ventilators that are constantly running thin, the medicine you need for those ventilators, the personal protective equipment, and the relief from the bullpen for our health care workers,” Murphy said.

Trump on Friday offered perhaps his most optimistic take yet on U.S. efforts to combat the spread of the coronavirus, and suggested the country could begin to reopen by May 1. The following day, he said his administration was examining how best to go about restarting the economy.

“People want to get back to work,” Trump said in an interview on Saturday on Fox News. “We are setting up a council of some of the most distinguished leaders in virtually every field, including politics, business and medical. And we’ll be making that decision fairly soon.”

Leading public health officials have outlined several steps that need to be taken before moving toward a reopening. Those include rapid, large-scale and widely accessible tests to both diagnose who has the infection and check for antibodies, to figure out who has already been exposed and has some degree of immunity. The public health work force would also have to be bolstered to identify and isolate people who might be contagious, and trace their contacts.

The commissioner of the Food and Drug Administration, however, broke from Trump’s bullishness on Sunday, hesitating in an interview on ABC to say whether the president’s May 1 goal of relaxing social-distancing guidelines was realistic.

“It is a target,” Commissioner Stephen Hahn said on “This Week.” “And obviously, we’re hopeful about that target. But I think it’s just too early to be able to tell that.”

Hahn also expressed sharp concern about the reliability of some of the antibody tests that have been quickly developed, without the usual FDA oversight. Those tests can detect whether someone has already been exposed to the novel coronavirus and might have immunity.

“I am concerned that some of the antibody tests that are in the market that haven’t gone through the FDA scientific review may not be as accurate as we’d like them to be,” Hahn said in a separate interview on NBC’s “Meet the Press.” “No test is 100 percent perfect. But what we don’t want are wildly inaccurate tests. Because, as I said before, that’s going to be much worse.”

Other members of the White House coronavirus task force have recently warned about antibody tests that have not been reviewed by the FDA for emergency use.

“I want to say very clearly that no one should rely on any of the antibody tests on the market that have not gotten a formal [Emergency Use Authorization] from the federal government — that means about 95 percent of them,” Brett Giroir, the Department of Health and Human Services’ testing czar, told reporters on Thursday.