Gov. Jerry Brown, who is both a fiscal hawk and an ardent supporter of Affordable Care Act, has already spoken about his skepticism of a single-payer program, saying it would be prohibitively expensive.

But at least one candidate running for governor next year plans to make universal health care a centerpiece of the campaign. Earlier this month Lt. Gov. Gavin Newsom said he was working with health care experts to craft a plan for a single-payer system. While he was mayor, the city approved a plan to offer universal health care for all of its residents.

Mr. Lara said the Republican defeat in Congress could pave the way for a single-payer system.

“It’s easier to expand health care than make up lost ground as we would have had to do,” he said. “We really have the chance to make universal health care a reality now.”

The proposal differs from existing programs in one big way: It would include all residents, regardless of their immigration status. Obamacare explicitly excluded undocumented immigrants from benefits of the program, though children in California can receive basic coverage even if they are undocumented.

Advocates of a single-payer program argue that it would bring down costs and encourage preventive care. But opponents say there would be less choice and efficiency in medical care, and that taxes would rise significantly for all residents.