People briefed on the matter said officials at the California Air Resources Board were amenable to the 2030 compromise, even as they coordinated with the state’s attorney general, Xavier Becerra, who was preparing a legal challenge in case the talks collapsed.

Also amenable to compromise are some of the automakers, who favor a more moderate approach to a regulatory rollback than the one favored by Mr. Pruitt. But “automakers are in different positions” on how to proceed, said one person close to their thinking, with some companies more focused on rolling back the standards through 2025, and others more eager to have a broader discussion on a compromise with California and standards through 2030.

A person close to the Trump administration said White House officials were also pushing the E.P.A. toward a compromise with California. The White House, this person said, is more in tune with concerns from some automakers who feel that the rollbacks they lobbied for have triggered an overzealous response from the E.P.A., bringing the federal government to the brink of a battle with California that could throw the entire auto market into disarray.

Mr. Pruitt has been a wild card, eager to score a clear victory in dismantling environmental regulations. In one sign of his zeal — and his apparent disconnect with the position of the auto industry — he has openly described the planned rewriting of auto emissions standards as a “rollback,” much to the chagrin of auto lobbyists who have long said that formulation does not accurately describe the changes they are seeking.

Big obstacles remain to reaching a compromise. California and E.P.A. officials have met at least three times in the last few months to discuss auto emissions regulations. The latest round of talks took place in California last week between Mary D. Nichols, chairwoman of the California Air Resources Board, and William Wehrum, the E.P.A.’s senior clean air adviser.

Image Mary D. Nichols, chairwoman of the California Air Resources Board, is negotiating with the E.P.A. Credit... Melissa Lyttle for The New York Times

A person close to the California negotiators characterized the meeting as “highly non-substantive,” even as he said a compromise remained possible when talks resumed. But a person close to the administration had a more positive take, calling the talks “productive.”