Five months later, as Mr. O’Rourke considers a run for president, his decision not to back Ms. Jones lays bare the go-it-alone streak that has defined his career, separating him from a modern Democratic Party that has prized near-uniform opposition to Republicans in Washington. While supporters view his above-the-fray message as the foundation of his appeal, he has left important Democratic constituencies wondering if he can be fully trusted as an ally.

“Beto-first politics,” said Jess Morales Rocketto, a Democratic operative who worked for Hillary Clinton in 2016. “He was concerned about Beto. I’m not sure he was concerned about building the future of Democratic politics.”

In Texas’s 23rd Congressional District, his choice was more than symbolic. Mr. Hurd won by fewer than 1,000 votes, and many voters and local activists hold Mr. O’Rourke — whose success helped lift down-ballot candidates across the state — largely responsible for Ms. Jones’s defeat.

“All I kept thinking was, wait, Beto is supposed to be helping us because he’s a Democrat,” said Rosey R. Abuabara, the leader of TX-23 Indivisible, which worked to oust Mr. Hurd. “I really felt like Beto was just getting in my way.”