So far those figures have not compared the number of deliveries to the number of equipment needed. And that gap seems huge.

Mr. Cuomo crystallized the issue on Tuesday when he said that “the timeline doesn’t work.”

“I don’t need ventilators in six months,” he said. “And I don’t need ventilators in five months, four months or three months.”

The reality is that timing is impossible, producers of the equipment say. For example, Medtronic, one of the leading manufacturers of ventilators, now makes about 225 of its high-end machines each week, up from 100 in more normal times. But it is a daunting task because there are 1,500 unique parts supplied from 14 countries. The company is aiming for 500 a week, a Medtronic spokesman said. Even that would not satisfy current demand.

Last week, Mr. Trump urged states to fend for themselves, looking for whatever they could find on the open market. But that only underlined how poorly prepared federal stockpiles were for a pandemic — a situation that the last three administrations had rehearsed in an effort to improve plans. The president’s comments set off a scramble that only accelerated the criticism of how the White House has handled the allocation of scarce supplies.

Gov. J.B. Pritzker of Illinois, a Democrat, argued that in sending each of the states off to find their own equipment, “we’re competing against each other, we’re competing against other countries.” The result, he said, was “we’re overpaying.”

Mr. Trump responded that Mr. Pritzker and other governors “shouldn’t be blaming the federal government for their own shortcomings. We are there to back you up should you fail, and always will be!”

But it is increasingly clear that the federal government will not be able to back up the states, at least at the scale needed, for the first wave of patients. And by letting companies voluntarily produce the necessary equipment, rather than under orders in the Defense Production Act, the administration is not responsible for whether the quotas are met, or if the output reaches hospitals.