“If we don’t flatten the curve, we’re on a trajectory currently to exceed our capacity in the New Orleans area for ventilators by about April the 4th, and all beds available in hospitals by about April the 10th,” Gov. John Bel Edwards, Democrat of Louisiana, said Sunday on “Meet the Press on NBC. “So we’re doing everything we can to surge capacity. It’s very difficult.”

Industry executives made the point that while the Defense Production Act enabled the White House to create the illusion of decisive executive action, it did not solve the nuts-and-bolts problem of gearing up scores of suppliers or creating Made-in-America production lines where few exist. That is the problem G.M. and Ventec, and other companies involved in the effort like Ford and Medtronic, are facing — often seeking parts from the same suppliers.

“We are moving full steam ahead on ventilators because they know there is an immediate need for increased production,” said Chris Brooks, Ventec’s chief strategy officer, even if it is still unclear whether the customers are hospitals, states or the Federal Emergency Management Agency, which the White House has delegated to take charge of the effort.

Mr. Trump came to this crisis belatedly, but once he did he has tried to portray himself as a wartime president, one who is making use of all of America’s talents to fight an invisible but devastating enemy. And in that regard, the best analogy may be Franklin D. Roosevelt’s “arsenal of democracy,” the phrase he used in a Dec. 29, 1940, fireside chat, as he tried to get American industry to support Britain in its fight with Nazi Germany, without getting the United States into the war.

It turned out to be prescient, because industry was already getting onto a wartime footing by the time Japan attacked Pearl Harbor a year later, plunging the United States into a manufacturing frenzy. That is when Ford began churning out B-24 bombers and Sherman tanks.

But in this case, Mr. Trump sought the language of wartime action without the responsibility for making it happen. He welcomed voluntary efforts that were already underway, as manufacturers like Medtronic and the Dutch manufacturing giant Philips promised to ramp up production. The problem was that it was uncoordinated — as if the Pentagon had announced it needed more missiles, more artillery shells and more nuclear weapons but left unclear how many or where they should be delivered.

That was the situation Mr. Kushner found when he entered the effort, at the request of Vice President Mike Pence. He moved the authority to deal with the issue from the Department of Health and Human Services to FEMA, saying that the latter agency knew how to act in a “battle rhythm.” But still, no one knew how many ventilators were already in the market, where they would be needed first or how many more companies could be expected to make. And it was complicated by the fact that many of the largest manufacturers had moved operations offshore, to Ireland, Switzerland and, of course, China.