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Senator Bernie Sanders of Vermont, under pressure from the Clinton campaign to explain how he would pay for his progressive policies, unveiled a universal healthcare plan on Sunday night that includes sweeping tax increases and a drastic tax hike for the wealthiest.

Ahead of a nationally televised Democratic presidential debate, Mr. Sanders said that his “Medicare-for-all” plan was in the spirit of Democratic presidents such as Franklin Roosevelt and Harry Truman and projected that the health savings would outweigh the higher taxes that would pay for the plan.

The Vermont senator’s proposal would be made possible by a 2.2 percent health care premium, calculated under the rules for federal income taxes and a 6.2 percent health care payroll tax paid by employers. Mr. Sanders would also impose an estate tax on the wealthiest Americans and make changes in the tax code to make federal income tax rates more progressive.

Under the plan, individuals making $250,000 to $500,000 annually would be taxed at a rate of 37 percent. The top rate, 52 percent, would apply to those earning $10 million or more a year, a category that in 2013 included only the 13,000 households in the United States.

“Universal health care is an idea that has been supported in the United States by Democratic presidents going back to Franklin Roosevelt and Harry Truman,” Mr. Sanders said in a statement on Sunday night. “It is time for our country to join every other major industrialized nation on earth and guarantee health care to all.”

Mr. Sanders’s proposal would expand Medicare and “build on the success of the Affordable Care Act,” he said. The senator said patients could choose their doctors and receive comprehensive care for various services, including hospital stays, emergency room visits and primary and specialty care.

Mr. Sanders said the plan would save $6 trillion over 10 years compared with the current system, citing an analysis by Gerald Friedman, an economist at the University of Massachusetts at Amherst who studies health care costs.

The typical family earning $50,000 a year would save nearly $6,000 annually in health care costs, Dr. Friedman calculated, according to the announcement. The announcement said the average working family now pays $4,955 in premiums for private insurance and spends an additional $1,318 on deductibles for care that isn’t covered. Mr. Sanders said a family of four earning $50,000 would pay $466 per year to this program.

He added that businesses would save more than $9,400 a year in health care costs and that the average annual cost to the employer for a worker with a family who makes $50,000 a year would go from $12,591 to $3,100. The plan would include savings “from reducing outlays for taxpayer-supported health care expenditures.”

Mr. Sanders’s campaign said the plan woulds cost an estimated $1.38 trillion per year and that a family of four, taking the standard deduction, can have income of up to $28,800 and not pay the health care tax.

Roberton Williams, a senior fellow at the non-partisan Tax Policy Center, estimated that the tax increase that Mr. Sanders is proposing would be the largest since World War II, increasing taxes by approximately $450 billion per year.

“It seems to be very, very large,” Mr. Williams said, noting that the highest earners would bear most of the pain.

Mr. Williams suggested that the cost estimates for that the Sanders campaign is using will require more scrutiny and that employers are likely to pass on the new payroll tax to consumers or employees in other ways. The political feasibility of imposing such a vast overhaul is also a concern.

“What he’s talking about is turning the government into the provider of health insurance,” Mr. Williams said, noting that the Obama administration would have been interested in a single-payer system if it could have passed Congress. “If you’re talking about replacing an entire industry with a federal government plan, that’s a big order.”

Hillary Clinton and Mr. Sanders have sparred in recent days as polls show a tight Democratic presidential race in both Iowa and New Hampshire.

As Mrs. Clinton has intensified her attacks on Mr. Sanders, he has rolled out policy details. On Saturday, Mr. Sanders announced that he was supporting legislation to amend a 2005 law on gunmakers’ liability that he voted for and that Mrs. Clinton has been using to attack him as weak on gun regulations.

Mr. Sanders has defended his support of the gun law by saying he was trying to shield small gun dealers who followed the law from expensive litigation. He also proposed an amendment to the legislation that would require the Commerce Department to monitor and report on the law’s impact in rural areas.

In an interview on Sunday before the release of the plan, Jeff Weaver, Mr. Sanders’s campaign manager, defended the idea of raising taxes on the middle class by saying families would save money through the single-payer program.

“It’s going to replace much larger expenses that you pay currently to the private sector,” Mr. Weaver said. “If I ask you to pay $5 in taxes and I save you a $100,000 in costs, am I raising your taxes? I guess technically I am, but really it is the net of what the effect is.”

On Sunday night before the debate, Mrs. Clinton’s issued a statement in response to Mr. Sanders’s plan, saying that he “has been changing a lot of positions in the last 24 hours because when his plans and record come under scrutiny, their very real flaws get exposed” referring to this plan and his support for the new gun legislation.

In a separate statement, Brian Fallon, a campaign spokesman, said that “after weeks of denying the legitimacy of the questions Hillary Clinton raised about flaws in the health care legislation, he’s introduced 9 times over 20 years, he proposed a new plan two hours before the debate.” He added: “When you’re running for President and you’re serious about getting results for the American people, details matter—and Senator Sanders is making them up as he goes along.”

