Washington (CNN) Of the four candidates who currently compose the top tier of the 2020 Democratic field, three have expressed support for "Medicare for All" -- a proposal that would eliminate the private health insurance industry in its entirety and replace it with a government-run system.

Vermont Sen. Bernie Sanders is the author of the Medicare for All legislation in the Senate. Massachusetts Sen. Elizabeth Warren said in the first Democratic debate that she supports the full elimination of the private health insurance industry. California Sen. Kamala Harris has been a bit all over the map on the issue; she raised her hand in the first debate to say she supported abolishing private health insurance totally, but then adjusted that position (I think) the following day.

Only former Vice President Joe Biden is clearly on the record as opposing the sweeping change that Medicare for All would institute. "I think one of the most significant things we've done in our administration is pass the Affordable Care Act," Biden said recently in New Hampshire. "I don't know why we'd get rid of what in fact was working and move to something totally new."

Which brings me to this question in an NPR-PBS-Marist national poll released on Monday: "Do you think Medicare for All, that is a national health insurance program for all Americans that replaces private health insurance, is a good idea or a bad idea?"

Just 4 in 10 (41%) say that Medicare for All is a good idea, while 54% said it is a bad idea. Which, well, uh oh.

Predictably, Republicans oppose such a proposal en masse, with 83% saying it's a bad idea. But the potential political trouble for Sanders, Warren and (maybe) Harris is that just 39% of independents think getting rid of private health insurance is a good idea. And even 3 in 10 self-identified Democrats are skeptical and call it a bad idea.

Now, this is one poll. Snapshot in time and all that. And supporters of Medicare for All can -- and will -- argue that the public's reaction to the idea is largely informed by misinformation put out by opponents.

Maybe! But the point remains: A proposal favored by three of the four leaders in the 2020 Democratic primary has the support of barely 40% of the public.