Sanders estimates a middle-class family of four would pay an annual premium of $466 under his plan, with no deductible or co-pays. Less affluent households would pay less than that, or nothing at all.

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But for at least 72 percent of households enrolled in Medicaid -- in which someone is working -- the costs of Sanders's plan would exceed the benefits, according to an analysis by Kenneth Thorpe, a public-health expert at Emory University.

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That figure includes 5.7 million households, or 14.5 million people -- among them, 4.2 million Hispanic recipients and 2.5 million black recipients. The requirements for eligibility for Medicaid vary widely by state, so that group includes some households living in poverty as well as some that are modestly better off.

"The vast majority of low-income Medicaid workers, who are probably predominantly minority, are going to end up paying more in terms of payroll taxes, and aren't going to receive really any financial benefits," said Thorpe, a former Clinton administration health official.

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Many lower-income people are already insured or eligible for insurance under Medicaid, at least in the states that expanded the program under President Obama's health-care reform. Many Medicaid beneficiaries also work, and those workers' wages would likely decline due to the additional 6.2 percent payroll tax the proposal would levy on their employers.

Thorpe has also argued that the senator from Vermont is underestimating the cost of his plan by roughly $1.1 trillion a year. Regardless of the cost, though, the plan would be detrimental for many poor households, he concluded.

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In calculating that 14.5 million Medicaid beneficiaries would be worse off, Thorpe used the campaign's more optimistic estimate of the cost. Using his own, more pessimistic estimate, the figure increased to 16.8 million.

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In an email to Wonkblog, Sanders's policy director, Warren Gunnels, said the candidate's plan would have other benefits for Medicaid recipients.

Research has found that some specialists currently refuse patients on Medicaid. Gunnels suggested that Sanders's plan would solve that kind of problem. For example, in a single-payer system, everyone would have federal health insurance, and it would be difficult for providers to deny patients on the federal plan without going out of business. "The reality is that people on Medicaid would see a substantial increase in the quality of care under Sen. Sanders' Medicare-for-all plan," he wrote.

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Any improvements in access would come at a cost for those households, Thorpe noted. "In terms of the financial piece of it, they would be the losers," he said.

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The effect on Medicaid beneficiaries who do not work would be limited, since they do not have employers who would be paying more in taxes. And there are some groups of Americans living in poverty, or close to it, whom the plan would arguably help.

The nonpartisan Kaiser Family Foundation has estimated that 2.9 million poor adults are ineligible for Medicaid because they live in states that did not expand the program. They are also ineligible for the federal subsidies that families living above the poverty level apply toward insurance under the Affordable Care Act. The law was drafted on the assumption that states would expand Medicaid, and did not extend those subsidies to people who would be eligible for the expanded program. Under Sanders's plan, those people would have a chance to enroll in governmental health insurance.

Another 8.8 million people are already eligible for Medicaid, but haven't signed up. Sanders's plan, in which all Americans are eligible, would presumably simplify the process, possibly encouraging some of these people to subscribe. If they work, though, they'd likely be better off financially signing up for Medicaid under the current system than if they enrolled under Sanders's plan.

Finally, there are those households whose income makes them ineligible for Medicaid, but for whom health insurance is a serious financial burden. In states that have expanded Medicaid, for example, a family of three is ineligible if their annual income exceeds about $28,000. Nonetheless, paying premiums and deductibles is difficult because of their modest incomes.

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Some might use subsidies made available by Obama's Affordable Care Act to help pay monthly premiums, but must pay exorbitant deductibles and coinsurance out of pocket if they need to see a doctor. Others, despite being eligible for a subsidy or even working for an employer who sponsors a plan, choose not to enroll.

"Even if there's a subsidy, their family resources are still stretched, and they really are having trouble figuring out how to afford the coverage," said Diane Rowland, an executive vice president at Kaiser. "How you get it, and what your share of the cost is, is going to be a big factor in whether you feel you can afford it or not."

Sanders has been making his case to these Americans in the lower-middle class by talking about the onerous out-of-pocket medical costs that even families with insurance often must pay. He makes the case that his plan would save them money. Sanders's opponents say those savings are illusory, and that the senator is underestimating the amount those families would have to pay in increased taxes to fund his system.

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In any case, these are the Americans whom Sanders's proposal has a chance of helping -- those who aren't impoverished, but who still can't afford the coverage offered by their employers or through the federal exchanges.

Note (Feb. 25, 10:47 a.m.): Gunnels, Sanders's policy director, wrote in an email to Wonkblog after this post was published that Sanders's health-care proposal is inseparable from the senator's call to raise the national minimum wage to $15 an hour. If Sanders were president, he would not allow his health-care proposal to become the law of the land if Congress did not also increase the minimum wage, according to Gunnels. "We would never allow that to happen," he wrote.

Gunnels wrote that the effects of the health-care plan should be considered alongside those of an increase in the minimum wage -- which, he argued, would improve standards of living for the working poor.