“When people try to accuse us of going too far left — we’re not pushing the party left,” she said, to raucous applause, “We are bringing the party home.”

On a two-day swing through Iowa this weekend Ms. Ocasio-Cortez and Mr. Sanders, the senator from Vermont, traversed the state in tandem, an unlikely duo separated in age by nearly half a century, spreading their ideology in an unlikely place. They held rallies in Council Bluffs on the state’s conservative western edge and in Coralville, near the liberal home of the University of Iowa. They hosted a climate change forum in Des Moines.

The trip was their first together since Ms. Ocasio-Cortez, 30, endorsed Mr. Sanders, 78, last month, a decision that immediately jolted the Democratic primary and injected fresh energy into his campaign. Less than three weeks after he suffered his heart attack, they held an enormous rally in New York City that both demonstrated his political strength and deflected attention away from his health and age.

Now, as Mr. Sanders reboots his campaign and prepares for an all-out push in Iowa, he is on a quest to lure the progressive left to him and away from Senator Elizabeth Warren of Massachusetts and to convince the country that they need a wholesale revolution rather than “big, structural change.”

In Iowa, having Ms. Ocasio-Cortez by his side could prove a powerful weapon, as he and Ms. Warren remain locked in an intense battle to win over progressive caucusgoers with political appeals and policy plans. Mr. Sanders’s campaign is confident that Ms. Ocasio-Cortez will help motivate young people, a group that was critical to his success in 2016 but is now also excited by Ms. Warren, as well as the entrepreneur Andrew Yang.