"Are we going to have the American Dream for your generation, or will it be squandered for you, before we even get a chance, by this generation?" he said.
Later Saturday, Ryan mingled with fans at Bowling Green State University in northwest Ohio before the Falcons took on his alma mater, Miami University.
Ryan was greeted by a friendly crowd at a tailgate party hosted by the College Republicans.
The only heckling he heard was "Go Falcons."
Ryan didn't make any formal remarks, and instead played a bean-bag toss game with his children and ate bratwurst and potato salad.
He met with students and the president of Bowling Green, leaving before the game started, and joked at one point about not seeing many Miami fans in the crowd.
The Republicans are hoping to energize Ohio's young voters this weekend as the campaign wraps up a week of crisscrossing the battleground state.
GOP presidential nominee Mitt Romney had an afternoon rally at Shawnee State University in Portsmouth in southern Ohio.
Associated Press Writer John Seewer in Bowling Green, Ohio, contributed to this report.