When President Trump came to office, he promised a new day with America’s manufacturers, casting himself as the first president who understood their needs. He toured factory floors, often handing out his signature “Make America Great Again” hats.

Yet in the first national crisis that required harnessing American manufacturing ingenuity and ramping up production of ventilators, perhaps the most crucial piece of equipment for patients in crisis, the White House’s ability to gather the power of American industry crumpled.

It was unable to communicate how many ventilators it would need or how quickly it would need them. Mr. Trump set states off on a mad scramble to find their own, leading to bidding wars against one another. Even today it is unclear who is deciding where the new American production will be directed — to the highest bidders or to the cities that need them most.

A week after praising General Motors and a small ventilator manufacturer, Ventec Life Systems, for their voluntary efforts to combine cutting-edge technology with G.M.’s expertise at supply chains and mass production, the president blew up at the world’s largest carmaker, accusing its chief executive, Mary T. Barra, of moving too slowly and trying to “rip off” the federal government. In fact, G.M. and Ventec had already signed a partnership — without government help — to ramp up production.

Interviews with White House officials, industry executives and outsiders who tried to intervene make two problems clear. Mr. Trump’s first mistake was recognizing the problem far too late, even though his own medical experts had identified a probable shortage of ventilators as a critical problem in late January, as panic set in that the virus was headed to the United States. Had the president acted sooner, thousands of new ventilators would probably be coming off production lines next month, when they are likely to be desperately needed.

And even after the problem was recognized, and the president’s son-in-law and senior adviser, Jared Kushner, took over the process, both the White House and the Federal Emergency Management Agency struggled to define what was needed, who would pay for it and how to solve the problem of supply chains that stretched across more than a dozen countries.

“We’re going to have plenty,” Mr. Trump said Friday afternoon, declaring that he was invoking the Defense Production Act, a Korean War-era law, to force the companies to make more. But he gave no numbers — and glided past the complexities of getting between 700 and 1,500 components from more than a dozen nations.

“It’s terrific that the administration is now beginning to use the D.P.A.,” said Joshua Gotbaum, a former defense official in the Clinton administration who often made use of the Defense Production Act. “Had they started two months ago, we would already have ventilators, masks and other critical equipment in mass production.”

“It is one thing to know that there should be a central national effort,” Mr. Gotbaum added. “It is quite another to accept the responsibility for the shortcomings and mistakes that will inevitably occur with it.”

“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 Phillips 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.

Along came G.M. and Ventec, a partnership Mr. Trump celebrated in a tweet a week ago. But all week the details languished. Early hopes that the company could produce 20,000 ventilators quickly began to fade; in the first few weeks, the figure was more like 5,000. And that production would not begin until late April, if everything went perfectly.

Still, a small group of White House officials briefed on the discussion anticipated that it would go ahead, a welcome announcement after weeks of headlines about the administration’s halting response to the spread of the coronavirus.

One administration official said that Mr. Trump had not been briefed on the details of the G.M.-Ventec deal, and that he was caught by surprise when he read a New York Times article about how the announcement was being held up while FEMA examined competing offers.

Instead of focusing on why the deal had been abruptly stopped, officials said, the president was enraged about the prospect of G.M. — which was actually Ventec’s subcontractor — trying to get money upfront from the government to fund suppliers. And aides told him that the company’s estimates of how many ventilators could be made in a relatively short period of time had shifted when G.M. officials were pressed.

So the president posted a series of tweets denouncing the company and its chief executive, urging them to build ventilators at a Lordstown, Ohio, plant that had been closed. (G.M. sold the plant last year and will be making ventilators in Kokomo, Ind., an electronics plant that has the clean rooms needed for manufacturing medical parts.)

Mr. Trump decided to go ahead and compel G.M. to manufacture the ventilators, but far fewer than the original deal envisioned. His attitude, officials said, was that since reporters had been pushing him on deploying the Defense Production Act, he would give them what they wanted — without giving G.M. the full deal. And then he named other firms that would also be tapped by FEMA.

But by the end of the weekend, it was still unclear what the production targets were or even if FEMA had issued any contracts. The companies did not know if Washington would take responsibility for distributing the ventilators.

In the Rose Garden on Sunday afternoon, Mr. Trump for the first time began to acknowledge the complexity of the undertaking American industry was just now beginning. “They are very complex,” he said of the machines. “You know, this is like building a car.”