“The speed and flexibility is breathtaking,” the executive said. “There’s no American plant that can match that.”

Though Americans are among the most educated workers in the world, the nation has stopped training enough people in the mid-level skills that factories need, executives say.

Eventually, the orbits of the men overlapped. “I’m not worried about the country’s long-term future,” Mr. Jobs told Mr. Obama, according to one observer. “This country is insanely great. What I’m worried about is that we don’t talk enough about solutions.”