The Pentagon is also making available 2,000 ventilators for hospitals, a number that would likely fall far short of the expected need. “When you look at how many people who may need it, 2,000 doesn’t put much of a dent into it,” Mr. Esper said.

While the military has infrastructure to help, there are limits. Field hospitals and the hospital ships Comfort and Mercy are designed for trauma wounds, not viruses, and doctors would have to be assigned from elsewhere to staff them. The ships, each with a 1,000-bed capacity, have helped in natural disasters like tsunamis, hurricanes and earthquakes, not quarantines.

Defense Department officials said that one possibility for the Comfort would be to station in New York Harbor and absorb non-coronavirus patients in New York, which could free up hospital beds in Manhattan to attend to infectious cases.

Gov. Jay Inslee of Washington said he spoke with Mr. Esper on Tuesday about getting access to resources that could help bolster new medical hospitals. “I would predict that we’re going to be getting real help from the Department of Defense,” Mr. Inslee said.

Part of the challenge is the unusual role Mr. Trump has assigned to FEMA, which traditionally is designated as the lead federal agency during major disasters to take requests from individual states and then assign other federal players to deliver on the pleas for help. In this case, Mr. Trump has left the Department of Health and Human Services in charge.

“FEMA is the only agency that has the full breadth of the federal government at its disposal,” said Daniel J. Kaniewski, who in January left FEMA, after serving since the start of the Trump administration as one of the agency’s top officials.

The disaster is so far-reaching, the federal government would never be able to address all of the requests for help, said W. Craig Fugate, who led FEMA during the Obama administration.