Billy Wynne, a health care lobbyist who used to work for Senate Democrats, said: “The literal meaning of ‘Medicare for all’ would include Medicare Advantage. But that is not what most supporters of Medicare for all have in mind.”

The champions of Medicare for all generally see insurance companies as part of the problem, not the solution.

“There are a lot of insurance companies and medical companies that are advocating for their own best interests, and those best interests are usually money, and not people’s health,” Representative-elect Deb Haaland, Democrat of New Mexico and a supporter of Medicare for all, said in an interview. “We need a national public health care system, which would be more affordable in the long run, and the outcomes might be better.”

Wendy Kaplan, 53, of Evanston, Ill., who has found family coverage under the Affordable Care Act rather expensive, said she liked the idea of Medicare for all.

“In principle,” said Ms. Kaplan, a Democrat, “I feel that health insurance should be available to everyone. Single payer is a great idea in principle. I don’t think health care should be a for-profit endeavor. My biggest reservation is whether our government could be competent at running something like that.”

Large majorities of Medicare beneficiaries say in surveys that they are satisfied with their coverage.

With a Republican president and a Republican-controlled Senate, proposals for a major new health care entitlement have no chance of becoming law in the next two years. But they show how an idea long relegated to the sidelines is edging back into favor with some Democrats and could be embraced by the party’s nominee in the next presidential election.