Do they? According to a poll from last month, 55% of Americans thought that if "Medicare-for-all" was put into place, they'd be able to keep their current health insurance (35% thought they would not, 10% didn't know). [1]

...That's despite the fact that earlier in the same poll, according to the methodology document, the questioner had asked their opinion about "having a national health plan, sometimes called Medicare-for-all, in which all Americans would get their insurance from a single government plan" and, separately, "creating a national government administered health plan similar to Medicare that would be open to anyone, but would allow people to keep the coverage they have if they prefer". Take from that what you will.

After noticing that weirdness, I looked for polls from other pollsters on the same subject. In an online poll from last October [3], when asked "When you hear candidates talking about 'Medicare for All', what do you think they are proposing?", 52% picked "A single, government-run health insurance program to cover all Americans", 21% picked "An optional government-run program that would compete with private insurance"... and 24% picked "Neither of these". That's roughly consistent with the other poll if you group "optional" and "neither" together, but I have no idea what people who picked "neither" think Medicare-for-all actually is.

Another relevant question is how many people support single payer or a public option when the choices are explained more clearly. Going back to the first poll, in the earlier question I mentioned before, 56% supported single payer, while 74% supported a public option. However, a later question asked "Would you favor or oppose a national Medicare-for-all plan if you heard that it would..." with a series of hypotheticals. One of those, "Guarantee health insurance as a right for all Americans", had 71% in favor; but "Require most Americans to pay more in taxes" and "Eliminate private health insurance companies" each had 37% in favor. (I suspect the authors of the NYTimes article had this poll in mind when they wrote "when people hear arguments against it, their support plummets".) Once again, the methodology is confusing: the question literally asks if the respondent would support (or oppose) Medicare-for-all as a whole if the hypothetical were true, but some probably responded based on whether they liked the hypothetical itself. That might help explain how "Eliminate private health insurance companies" polled worse than "having a national health plan [..] in which all Americans would get their insurance from a single government plan" from earlier. Another part of the explanation is probably just ignorance and people not thinking about the issue very hard.

From the second poll, when asked which option they would favor most, single payer, public option, and "neither" were all roughly tied, at 34%, 33%, and 30% respectively. The first two add up to 67% preferring either single payer or a public option. This is close to the 74% who supported a public option in the other poll, which makes the results roughly consistent, assuming that respondents to this poll who preferred single payer would still prefer a public option to nothing.

Anyway... it's certainly true that single payer has substantial support, and that it seems a lot more politically feasible today than it did in 2016, in large part due to the efforts of Bernie Sanders and others. But it's likely all downhill from here. Medicare-for-all has become such a popular rallying cry on the left that it doesn't have much room to grow. And for any variant of Medicare-for-all (like anything else), once a concrete policy is on the table and its costs and downsides are available to criticize, support will fall; and once conservative figures leap on the opportunity to rally the base with that criticism, what bipartisan support currently exists will evaporate. That doesn't mean it can't maintain enough momentum to become a reality: it could. But it will help to have a higher starting point of popularity, and so evaluations of "political feasibility" do matter.

[1] https://www.kff.org/slideshow/public-opinion-on-single-payer...

[2] http://files.kff.org/attachment/Topline-KFF-Health-Tracking-...

[3] https://www.axios.com/medicare-for-all-poll-midterm-election...