For now, as Ms. Warren demonstrated, many candidates do not want to wrestle publicly with the details. After Ms. Harris’s comment, her aides hastened to add that she would also support less sweeping changes to health care; like most other candidates, Ms. Harris declined an interview request. And by Friday, Mr. Booker, hours after announcing his presidential bid, sought to curtail the matter by offering a brisk “no” when asked if he supported eliminating private coverage.

Yet there is one likely 2020 contender who is thrilled to discuss Medicare for all.

Mr. Sanders, in an interview, did not mince words: The only role for private insurance in the system he envisioned would be “cosmetic surgery, you want to get your nose fixed.”

“Every candidate will make his or her own decisions,” Mr. Sanders said, but “if I look at polling and 70 percent of the people support Medicare for All, if a very significant percentage of people think the rich, the very rich, should start paying their fair share of taxes, I think I’d be pretty dumb not to develop policies that capture what the American people want.”

But Michael R. Bloomberg, the former New York City mayor who is considering a 2020 bid on a centrist Democratic platform, said it would be folly to even consider a single-payer system. “To replace the entire private system where companies provide health care for their employees would bankrupt us for a very long time,” Mr. Bloomberg told reporters in New Hampshire on Tuesday.

The Congressional Budget Office has not scored Mr. Sanders’s Medicare for All bill, but a study last year by the Mercatus Center of George Mason University predicted it would increase federal spending by at least $32.6 trillion over the first decade. The cost could be even greater, the study says, if the bill overestimated the projected savings on administrative and drug costs, as well as payments to health care providers.

The divide between Mr. Sanders, a democratic socialist, and Mr. Bloomberg, a Republican-turned-independent-turned-Democrat, reflects the large chasm in a party that has been reshaped by President Trump.

The president’s hard-line nationalism has simultaneously nudged Democrats to the left, emboldening them to pursue unambiguously liberal policies, and drawn independents and moderate Republicans to the party because they cannot abide his incendiary conduct and demagogy on race. These dueling forces have created a growing but ungainly coalition that shares contempt for Mr. Trump but is less unified on policy matters like health care.