PHILADELPHIA — Hillary Clinton spoke slowly, as if instructing an early-morning seminar, as she stared out at a roomful of students.

She extolled the virtues of a tax credit plan tied to paid apprenticeships, seeming to test a few attention spans. She shouted the name of Senator Bernie Sanders of Vermont, and the crowd shouted back, more loudly than it had before then.

And as Mrs. Clinton concluded a half-hour address here, aimed at young voters who have often proved resistant to her overtures, her tone grew urgent, almost pleading.

“I need you,” Mrs. Clinton said, amid the chandeliers and regal wood paneling of a hall at Temple University. “I need you as partners, not just for winning this election, but for driving real change.”