OMAHA, Neb. — Joe Biden slowly but steadily walked onto the stage in Omaha on Friday. As he did, 800 people in the downtown Hilton ballroom rose to their feet cheering.

“Did you see the results Tuesday?” he asked, igniting another round of cheers as he listed Democratic victories from governorships in New Jersey and Virginia to the mayoral seat in New York to a redistricting decision in California.

It was a joyful return to the political stage for the former president, whose party's effort to remain in the White House was rejected just over a year ago. Mr. Biden called for a political comeback, though not for himself, but to an audience hungry for a fight.

“You know what it feels like to be outnumbered,” he told Democrats in Nebraska, where Republicans have carried the state in every pr

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