The shortage of ventilators has emerged as one of the major criticisms of the Trump administration’s response to the coronavirus. The need to quickly equip hospitals across the country with tens of thousands more of the devices to treat those most seriously ill with the virus was not anticipated despite the Trump administration’s own projection in a simulation last year that millions of people could be hospitalized. And even now, the effort to produce them has been confused and disorganized.

At the center of the discussion about how to ramp up the production of ventilators is Jared Kushner, the president’s son-in-law and a senior White House aide, who has told people that he was called in two weeks ago by Vice President Mike Pence to produce more coronavirus test kits and who has now turned his attention to ventilators.

He has been directing officials at FEMA in the effort. Two officials said the suggestion to wait on the General Motors offer came from Col. Patrick Work, who is working at FEMA. Some government officials expressed concern about the possibility of ordering too many ventilators, leaving them with an expensive surplus.

As the agency has sorted through offers, trying to weigh production ability and costs, hospitals in New York and elsewhere are reporting a desperate need for more ventilators, which are critical in treating respiratory problems in a fast-rising tide of severe coronavirus cases.

A spokeswoman for FEMA said Colonel Work presented information on each contract in such meetings but did not make any recommendations. A White House spokesman declined to comment.

The involvement of General Motors was first floated this month as the carmaker’s factory floor in Kokomo was grinding to a halt and workers were being sent home — partly because the market was collapsing but also because workers would otherwise risk exposure to the coronavirus.

Last week, General Motors, Ventec Life Systems and a coalition of business executives called StopTheSpread.org issued a statement saying that Ventec would “leverage G.M.’s logistics, purchasing and manufacturing expertise to build more of their critically important ventilators,” including some portable units.