For months, President Trump had been putting pressure on the chief executive of General Motors, Mary T. Barra, because she had decided to idle an Ohio factory and lay off 1,600 workers. “I am not happy that it is closed when everything else in our Country is BOOMING,” he said on Twitter. “I asked her to sell it or do something quickly.”

In early May, it seemed an answer was at hand. From her spacious office on the 39th floor of the Renaissance Center in Detroit, Ms. Barra called the president on May 8 to update him. The automaker was in negotiations to sell the plant in Lordstown, Ohio, to a new company affiliated with a little-known electrical vehicle maker called Workhorse.

G.M. planned to announce the talks that afternoon along with a $700 million investment elsewhere in Ohio. But Mr. Trump beat the company to the punch, posting on Twitter that the Lordstown sale was practically a done deal. It wasn’t — but that was the least of the problems with what the president said.

The new venture, whose name remains secret, exists almost entirely on paper. Headed by the founder and former chief executive of Workhorse, Steve Burns, the business would have to raise at least $300 million to get Lordstown running again.