Presidential contender Elizabeth Warren infuriated America's wealthiest individuals when she unveiled her wealth tax proposal earlier this year, which would tax them 3 cents on every dollar over $1 billion in net worth.

Now, seeking to pay for an overhaul of the nation's health-care system, she's calling on them to pitch in a bit more.

The Massachusetts senator on Friday called for a doubling of her billionaire wealth tax as part of a new "Medicare for All" proposal, from 3% to 6% on wealth over 10 figures.

Warren's wealth tax proposal would also impose a 2% tax on net worth between $50 million and $1 billion. She has previously said that it would be used to fund her ambitious climate agenda, a slate of investments in child care and reductions in student loan debt.

But Warren is looking to avoid taxing the middle class in her latest plan. She released an analysis produced by several respected economists on Friday that suggests she will not have to.

Former IMF Chief Economist Simon Johnson, former Labor Department Chief Economist Betsey Stevenson, and Mark Zandi, chief economist at Moody's Analytics, wrote that Warren could pay for her program "without imposing any new taxes on middle-class families."

The economists cite a number of possible revenue and spending options that they found could generate $20.5 trillion in additional funding. Much of that funding is expected to come from reallocating employer spending on health care and taxing the increased take-home pay that employees are expected to receive under her system.

But taxes on the wealthy form a substantial portion. Doubling the billionaire wealth tax will raise $1 trillion over 10 years, the economists found. They note in their analysis that the calculation assumes a 15% rate of tax avoidance.

All told, Warren said her approach, over a decade, would cost the country "just under" the $52 trillion estimated price tag of the current system.

The tax hike plan comes as Warren and her campaign spar with members of the so-called billionaire class. On Thursday, the campaign tussled publicly with financier Leon Cooperman, who wrote Warren a letter accusing her of treating him like "an ungrateful child."

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Warren has been unfazed by the criticism from America's billionaires, who number fewer than 1,000 in total, as she continues to ascend in the Democratic primary contest while calling on them to pay more. Her move Friday shows that she is unlikely to reverse course.

Read more: The Supreme Court could stop Elizabeth Warren's wealth tax dead in its tracks

"Yes, billionaires will have to pay a little more, but they will still likely pay less than what they would earn just from putting their assets into an index fund and doing nothing," Warren wrote in her plan released Friday.

The proposal was unveiled after weeks of pressure on the New England progressive to release the specifics behind her health-care plan. Ahead of the plan's release, Warren had largely dodged answering whether her proposal would require taxing middle-class families.

Economists, even progressives, argued that a plan of the scale that Warren was describing would necessitate such unpopular measures. Sen. Bernie Sanders, a fellow presidential contender and author of a Medicare for All bill which Warren has co-sponsored, said such hikes would be required, though offset by reduced health-care costs.

Warren's plan also calls for other taxes likely to affect the wealthiest Americans. A proposal to tax capital gains like income for households in the top 1% would raise $2 trillion over 10 years, the economists wrote. And, they wrote, two new taxes on financial firms, a transactions tax and a "systemic risk fee," will generate $900 billion.

The economists note that their analysis "is not an endorsement of Medicare for All or of these proposed revenue and spending options to fund it."