With Republicans in full control of the federal government, there is no prospect that Democrats can put in place a policy of government-guaranteed medicine on the national level in the near future. And fiscal and logistical obstacles may be insurmountable even in solidly liberal states like California and New York.

Yet as Democrats regroup from their 2016 defeat, leaders say the party has plainly shifted well to the left on the issue, setting the stage for a larger battle over the health care system in next year’s congressional elections and the 2020 presidential race. Their liberal base, emboldened by Senator Bernie Sanders’s forceful advocacy of government-backed health care last year, is increasingly unsatisfied with the Affordable Care Act and is demanding more drastic changes to the private health insurance system.

In a sign of shifting sympathies, most House Democrats have now endorsed a single-payer proposal. Party strategists say they expect that the 2020 presidential nominee will embrace a broader version of public health coverage than any Democratic standard-bearer has in decades…

“There is a cultural shift,” said Ms. DeMoro, who was a prominent backer of Mr. Sanders. “Health care is now seen as something everyone deserves. It’s like a national light went off.”