Marriages and longtime friendships have been killed off by long road trips, so it was no certainty that the American political process could survive 24-plus hours in a Chevy Impala. But Representative Beto O’Rourke, Democrat of El Paso, suggested to his colleague and congressional district neighbor, Representative Will Hurd, a Republican, that they give it a try.

The two men had been visiting veterans’ service centers in San Antonio over the weekend when Mr. Hurd learned that his flight back to Washington had been canceled because of the winter storm.

Mr. O’Rourke was not sure his flight would make it either. So he proposed something of a political stunt: Why not rent a car together — two politicians from opposite parties, from politically pugnacious Texas, of all places — and broadcast their trip to Washington as a live bipartisan town hall?

Mr. Hurd, in a joint interview from the road, emphasized that the whole thing had been Mr. O’Rourke’s idea. “Beto suggested it; he thought I was going to say no,” Mr. Hurd said. He pointed out that in addition to their political disagreements, the two had very different philosophies when it came to road trips: Mr. Hurd liked to make a lot of stops; Mr. O’Rourke would drive nonstop through the night if he could.

But early Tuesday morning, they met at the Dollar Rent A Car and picked up a car, and the town hall began. Their near-constant live stream on Facebook had a nostalgic cable TV public-access feel, with a significant share of commenters suggesting technical fixes (which were not made), traffic diversions and places to eat.

The commenters threw some real political meat for the congressmen to chew on, as well. A large share of the discussion centered on health care reform: the relative virtues and shortcomings of the Affordable Care Act compared with the Republican plan to replace it. Both agreed that health care delivery needed to work better, though the devil remained in the unworked-out details.

Neither congressman sits at his party’s extreme, so their comity was not as surprising as it might have been on a Ted Cruz-Bernie Sanders road trip. Mr. Hurd, for instance, is not a fan of President Trump’s travel ban or his proposed border wall.

But they have clear differences of opinion, and in this politically contentious moment, Mr. O’Rourke said, high-profile bipartisanship is not always looked upon favorably. He mentioned as an example the scolding he got from a colleague for working on an immigration bill with a Republican, Steve Pearce of New Mexico, whose seat the Democrats want to win back. Mr. Hurd’s border district is another one Democrats are eager to reclaim, and the state Democratic Party sent out a news release on Tuesday declaring that giving the “appearance of bipartisanship is not a hall pass to avoid answering tough questions” about Trump policies.

Commenters, for their part, generally seemed to enjoy the trip. “This bromance makes me so happy,” one wrote. Another added more ominously, “Love the Thelma and Louise vibe.”

But a look at the congressmen’s Facebook pages showed that disagreements were still very much alive.

“Steve King is a horrible human being,” a commenter wrote on Mr. O’Rourke’s page, referring to the Iowa congressman whose recent remark on Twitter, “We can’t restore our civilization with somebody else’s babies,” drew the praise of neo-Nazis.

“Steve King is right,” said a commenter on Mr. Hurd’s Facebook page. (Mr. Hurd called Mr. King’s comments “unhelpful.”)

But the men would have plenty more time to talk about politics in the many, many more hours on the road, and in the legislative chamber that awaited them on their arrival Wednesday. Some issues were more immediate.

“Should have taken Hwy 79,” wrote one engaged citizen. “I-35 is the worst.”