LONGVIEW, Tex. — Beto O’Rourke was racing left again, insisting he knew what he was doing.

“Hydroplaning there a little bit,” he said softly, doing 75 in the passing lane through an East Texas downpour, double-fisting beef jerky in his silver pickup.

This self-assurance was understandable. In his campaign against Senator Ted Cruz, Mr. O’Rourke has been attempting the Texas equivalent of walking on water — winning statewide as a liberal Democrat — without yet losing his balance. There is bipartisan consensus, including from Mr. Cruz, that Mr. O’Rourke could actually prevail in November — maybe — if the blue wave crests just so. And now, 15 days into a 34-day road trip, Mr. O’Rourke was 50 miles from another disarmingly large crowd in a typically red county, primed to cheer his calls for brash progressivism deep in the heart of Trump country.

New gun restrictions. Fifteen-dollar minimum wage. Marijuana offenses expunged from arrest records.

“This moment, this year, this time is not easy,” Mr. O’Rourke thundered once he reached the stage, by turns swearing playfully in two languages to make his case. “It’s not for the faint of heart.”

But why not try? This is Texas, he reminded them. Or it can be.

For a quarter century now, a blue Texas has seemed both inevitable and impossible, the central political contradiction in a state defined by them — where conservatives joke that the best thing about Austin, the left-leaning capital, is its proximity to Texas; where the largest American flags are often flown by those agitating for outright secession.