“Our contention is that if no one’s ever shown up, and listened to you, and incorporated your story into why they’re campaigning, and the expectations that we’re setting for one another, then I wouldn’t expect you to vote either,” O’Rourke told Smith on Saturday.

So instead of centrist triangulation, O’Rourke — like Abrams and Gillum — is speaking to the aspirations of his base, and betting that other voters will be won over by his honesty. He defended the right of N.F.L. players to take a knee during the national anthem to protest police killings of unarmed African-Americans, supports “Medicare for All,” and slams Cruz for being in the pocket of the National Rifle Association. He’s campaigning in a conservative state, but refusing to let the right set the terms of debate.

It’s been working better than anyone could have expected. Though O’Rourke is still an underdog — Texas hasn’t had a Democratic senator in 25 years — pollsters describe the race as a tossup. He has raised record-breaking sums without taking any money from political action committees. Soon his campaign will announce its third-quarter fund-raising results, and the rumor is that the total will be staggering, though all O’Rourke would say on stage is that it’s “a lot,” and more than the $10.4 million he raised last quarter.

It helps that he seems to have the support of legions of urban and suburban women who abhor Donald Trump, some of whom, said Allison, have only recently “come out of the Democratic closet.” These women “know how to fund-raise,” she said. “They’ve been doing it for their fancy charities all their lives.”