Henderson, Nev.

It’s just after 9 a.m. Saturday, and Sen. Amy Klobuchar is testing a new joke. “We are suddenly seeing what we call a ‘surge,’ ” she says. “I got a text that had a bad autocorrect from a friend a few weeks ago. It said, ‘Congratulations on your insurgency.’ ” It’s a big laugh line for the audience of seniors and young families in this Las Vegas suburb.

Yet...