One possible sign of progress in widening his coalition is that former supporters of Senator Elizabeth Warren, who dropped out of the Democratic presidential race last week but has yet to make an endorsement, were not hard to find in the Sanders multitudes. One of them, Tom Sapkowski, said, “I don’t think Biden’s a hard enough left turn.”

Mr. Sapkowski, who worked 35 years “turning wrenches” as an auto mechanic, has lived the contradictions of the American economy, where unemployment is low but incomes for those who aren’t rich feel like they’ve flatlined. “Things have not changed for the middle class for the past 50 years,” he said. He remembered “during the Clinton administration where I made like 80, 90 grand, but apparently that was too much.”

His wife, Kim, who lost her job as an education administrator in January, said: “I was just thinking this morning, my dad, he was 58 when he retired from the telephone company. He had a very nice retirement. Belonged to the union. And here I am 55 and nowhere near to retiring.”

Younger voters often brought up the huge burden of college debt for their generation, which Mr. Sanders proposes to cancel.