Democratic governors blasted the Trump administration Sunday for not doing enough to help them battle the coronavirus outbreak, and one said more Americans will die because the president failed to act early.

Illinois Gov. J.B. Pritzker blamed Mr. Trump for not building up medical stockpiles two months ago.

“If they had started in February building ventilators, getting ready for this pandemic, we would not have the problems we have today and, frankly, very fewer people would die,” Mr. Pritzker told CNN’s “State of the Union.”

The president fired back Sunday evening in a hastily scheduled coronavirus task force briefing.

“He’s always complaining. We’re building a 2,500-bed hospital in McCormick Place. It’s a big convention center in Chicago. And we’re helping to staff it and probably will end up staffing it because he’s not able to do what you’re supposed to be able to do as a governor,” the president said.

Mr. Trump rattled off a list of supplies being sent to various hard-hit states, including 200 ventilators to Louisiana, 300 ventilators to Michigan, 500 ventilators to New Jersey and 600 ventilators to Illinois.

“Just think about that: 500 ventilators. A ventilator is a big deal,” the president said at the briefing, which hadn’t been planned as of early Sunday afternoon.

The group of state executives took to the Sunday talk shows to press for a national stay-at-home order.

Nine states have only limited measures to keep people off the streets, and five of those states — Arkansas, Iowa, Nebraska, North Dakota and South Dakota — have no stay-at-home orders at all.

One of those state governors without a mandatory self-isolation policy, though, echoed the calls for a more organized system for obtaining personal protective equipment and medical supplies.

Arkansas Gov. Asa Hutchinson, a Republican, said procuring medical equipment is like a “global jungle” with states outbidding one another for necessary items to counter the spread of COVID-19.

“I’d like to see a better way,” he told NBC’s “Meet the Press.” He said being outbid on supplies “has been challenging for us, but we recognize the federal government has said we are your backstop, you have to get out there and compete.”

Mr. Trump has repeatedly said the national stockpile of medical supplies — most notably ventilators — is to serve as a backup for states. He put the bulk of the responsibility on governors to prepare for and combat COVID-19.

The president has touted his early move to close the country’s borders to China and then eventually extending that ban to European states plagued with the pandemic.

The administration also built field hospitals in several states and sent Navy hospital ships, one to California and one to New York, the state hardest hit by the pandemic. The federal government is also shipping hundreds of ventilators to states as needed.

Still, federal officials warn that the next two weeks could be catastrophic in terms of deaths and urge all Americans to practice social distancing and stay at home.

“The next week is going to be our Pearl Harbor moment. It’s going to be our 9/11 moment. It’s going to be the hardest moment for many Americans in their entire lives,” Surgeon General Jerome Adams said on NBC’s “Meet the Press.”

The Centers for Disease Control and Prevention projects 100,000 to 200,000 deaths in the U.S. from COVID-19, even if social distancing policies and quarantine orders remain in place.

In New York City, the U.S. military set up a 2,500-bed hospital at the Javits Convention Center that is expected to relieve health care systems running at capacity. The USNS Comfort, a hospital ship, is docked in the city to treat patients.

New York state, with a population of more than 20 million, has had more than 4,000 deaths from COVID-19, but Gov. Andrew Cuomo said Sunday that the 24-hour fatality numbers had dipped for the first time. He cautioned that the drop, from 630 to 594, could just be a “blip” and said rapid testing and understanding when it is safe for people to return to work are key to getting life back to normal.

“I hope we are somewhere near the apex … or we are somewhere near the plateau,” Mr. Cuomo told reporters.

The virus, which first emerged in Wuhan, China, spread to more than 1.2 million cases around the world and has taken more than 66,500 lives, though most people who contract the illness will recover. According to Johns Hopkins University, about 260,000 people worldwide have recovered from COVID-19.

As of Sunday, the U.S. had more than 312,000 cases, 8,500 fatalities and almost 17,000 reported recoveries.

The virus hasn’t spread as rapidly in Arkansas as it has in hard-hit places such as New York, Louisiana and Michigan.

Michigan, with a population of 10 million, now has the third most recorded COVID-19 cases in the U.S. As of Sunday, it had more than 14,000 cases and 540 deaths.

Michigan Gov. Gretchen Whitmer, a Democrat, said hospitals in her state are at capacity and lack personal protective equipment for health care workers.

“We don’t have enough tests,” she said. “It is an issue across the country.”

She said the administration sent 300 ventilators to Michigan but added that a national stay-at-home order would be better than a patchwork approach.

“Not having a national strategy where there is one strategy for the country is creating a more porous situation where COVID-19 will go longer,” she told “Fox News Sunday.”

Louisiana Gov. John Bel Edwards, a Democrat, said his state will likely exceed its ventilator capacity Thursday and that acquiring ventilators has been a major problem.

Washington state, the first hot spot for COVID-19 in the U.S., has reduced the number of cases. Gov. Jay Inslee, a Democrat, said a lack of testing is a problem nationally and that the president should use the Defense Production Act to order companies to make ventilators.

“We governors — Republicans and Democrats — have been urging the president to do what he should, which is if he wants to be a wartime president show some leadership, mobilize the industrial base of the United States. That is what we need,” Mr. Inslee said on NBC’s “Meet the Press.”

Mr. Trump invoked the Defense Production Act on Thursday.

But the White House team insisted during Sunday evening’s briefing that there is hope.

Taskforce coronavirus coordinator Dr. Deborah Birx said new cases and deaths from COVID-19 are declining in Italy and Spain, “giving us hope of what our future could be.”

“I want to say to the American people that we are beginning to see the glimmers of progress,” said Vice President Mike Pence, who heads the task force. “The experts will tell me not to jump to any conclusions, and I’m not. But, like your president, I’m an optimistic person and I’m hopeful. The truth is, we’re starting to see cases and most importantly … hospitalizations beginning to stabilize.”

• Dave Boyer contributed to this report.

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