The auto industry, embracing Mr. Trump’s promise of a more industry-friendly administration, has lobbied aggressively for a relaxation of the strict Obama-era rules. But the administration ultimately went well beyond what the industry was seeking.

The administration’s proposed fuel-economy rollback goes so far, in fact, that California and a dozen other states have said they will retain the stricter rules, threatening to split the United States auto market in two. Automakers are also facing a public backlash over their calls for looser pollution rules: Sierra Club, the environmental group, said this week it had delivered a petition with more than a quarter million si gnatures opposing the rollback to Ford’s headquarters.

“Here we have a president who made a political decision and is about to browbeat industry to fall in line,” said David Friedman, the acting administrator of the National Highway Traffic Safety Administration under President Barack Obama who is now director of cars and product policy at the Consumers Union, an advocacy group. “It indicates how political this is as opposed to analytical.”

The automakers now find themselves walking a tightrope.

On one hand, they are eager to stay in the good graces of a president who not only is intent on moving forward his deregulatory agenda, but who is also capable, if so inclined, of hurling insults at automakers on Twitter or pushing for damaging tariffs. At the same time, automakers are eager to find a way to work with California, which is intent on sticking with the Obama-era rules and has threatened to sue if the federal government gets in the way.

In recent days, auto-industry representatives quietly met with senior White House officials to prepare for Friday’s planned gathering. In one sign of the uncertain path ahead, there are differing assessments of the White House’s message to carmakers in that meeting.