Chelsea Clinton made an astonishing claim at a campaign event for her mother last week: Bernie Sanders has a plan that could cost millions of Americans access to their health insurance.

"Sen. Sanders wants to dismantle Obamacare, dismantle the CHIP program, dismantle Medicare, and dismantle private insurance," she said during a campaign stop in New Hampshire, according to NBC News. "I worry if we give Republicans Democratic permission to do that, we'll go back to an era — before we had the Affordable Care Act — that would strip millions and millions and millions of people off their health insurance."

The attack echoes an argument the candidate herself has been making. "[Sanders] wants to roll Medicare, Medicaid, the children's health insurance program, the Affordable Care Act program, and private health insurance into a national system and turn it over to the states to administer," Hillary Clinton said in Ames, Iowa. "I think that would be a big problem."

The context here is that Clinton doesn't support single-payer health care. Sanders does. And so do many liberal Democratic primary voters. So Clinton is attempting something risky: an attack, from the left, against Sanders, whose support for publicly provided health care is much more fulsome than Clinton's.

Sanders is rising in the polls — and the Clinton campaign is on the attack

As primary season nears, Sanders has seen a surge in his poll numbers. A CBS News/NYT national poll showed Clinton's lead narrowing from 20 percentage points to 7 over the past month. Vox's Andrew Prokop spent last week in Iowa, which will host its caucus February 2, and says it's a similar story:

Out away from the Washington, DC, bubble — where it's been taken for granted for years that Clinton will win and has to win — liberal-leaning Iowans are seriously thinking about which candidate better represents their values and their ideals, and about which candidate has a better shot at bringing about the major change they feel is still necessary. And many of them are concluding that Bernie Sanders is that candidate.

Part of that calculation comes from Sanders's more full-throated embrace of a liberal agenda: He wants to break up the big banks, extend Medicare to all, and make college tuition free.

At the core of Sanders's ideas on health care is a relatively simple idea: All American residents should receive a health insurance plan from the government.

This is a more radical idea than Obamacare, which, while it did expand insurance access, still leaves 35 million people uncovered. Sanders has, for decades now, pushed on the idea that this is unacceptable and that all Americans ought to have coverage.

"Health care, to my mind, is a right of all people," Sanders told my colleague Ezra Klein. "That's what I believe. I think every man, woman, and child is entitled to health care, and that right exists in virtually every other major industrialized country on Earth."

Sanders's 2013 health care plan — and its problems

The Clinton campaign, however, is trying to convince Democratic voters that Sanders's plans are unrealistic, poorly constructed, or both. To do so, they've dug into a bill Sanders introduced in 2013 that outlines what a single-payer system in America could look like.

The bill envisions each state using federal funds to set up a public health plan. (This is basically how the Canadian health system works.) If the state doesn't create a plan, the federal government will intervene and take over the task.

Clinton is attempting something risky: an attack, from the left, against Sanders

Sanders's bill also stipulates that the federal government will pay for, at most, 91 percent of the cost of each state's plan — leaving the state to cover the last 9 percent. So the Clinton campaign argues that "millions" could lose their health insurance if Republican governors left their new, single-payer plan to the feds and didn't contribute their 9 percent.

The Clinton campaign's argument is interesting, but it's the kind of thing that would get worked out through the legislative process. The broad point that Clinton's campaign is trying to obscure is that Sanders wants to move the country all the way to a single-payer system, in which everyone would have government-provided health insurance, and Clinton doesn't.

Sanders's idea might be a bad one, or an unrealistic one, but it's genuinely strange for the Clinton campaign to try to paint it as somehow contrary to the cause of government-provided health insurance.

Clinton is avoiding attacking single-payer itself – and with good reason

Health care is a tricky space for Clinton to navigate in the Democratic primary. So far, her campaign hasn't attacked the idea of a single-payer system itself, and for good reason: The idea is wildly popular among the kind of liberal voters Clinton needs to win the Democratic primary. One recent poll finds that about 80 percent of Democrats like the idea of a single-payer system.

Her campaign is clearly cognizant of this fact, and attempting to walk the line between criticizing Sanders's proposal and the idea of government-run health care itself.

"Secretary Clinton absolutely respects Democrats who support the principle of a single-payer system; she counts many of them among her supporters," Clinton senior policy adviser Jake Sullivan told reporters Wednesday. "She also believes many of those people would agree with her that now is not the moment to plunge the country back into a divisive debate over health care."

At the end of the day though, the fight Clinton and her campaign picked only underscores the thin line they're walking. Clinton is the candidate who doesn't want to alienate single-payer supporters, and Sanders is the candidate who actually supports single-payer health care. That's a real difference between the two, and one that leaves Clinton vulnerable with liberal primary voters.