EL PASO — Beto O’Rourke attracted the officers’ attention near the Texas-New Mexico state line, rocketing past them in a speeding Volvo, hustling to nowhere around 3 a.m.

He was so inebriated when the police reached him — after he had collided with a truck and pivoted to a stop across the center median of Interstate 10 — that he nearly collapsed when he tried to step out of the car.

Hours earlier, on Sept. 26, 1998, Mr. O’Rourke had turned 26. He was home again in El Paso, back for good after three searching years of post-college odd jobs in New York City. He had moved into an apartment near his parents, in an 18-unit building his family owned. His mother hired him to help with computers and inventory at her home-furnishings store. His father, a hard-charging former local politician, was dreaming bigger.

And an after-hours mistake, even one this serious, was not going to stand in the way.

“I remember he came home afterward; we were talking about it,” his mother, Melissa O’Rourke, said of the arrest. “It was just very, ‘How could I be so stupid?’”