(CNN) Sen. Bernie Sanders on Tuesday unveiled plans for a hefty tax on the ultra-rich that he says will pay for several of his expensive social spending proposals, including part of "Medicare for All."

Sanders, a Vermont independent, has come under fire from a number of his 2020 Democratic presidential primary rivals over the cost of his plans, which would run into the trillions of dollars. While he has maintained that the wealthy would foot the bill for most of those proposals, Sanders has acknowledged that the middle class would see their taxes rise to pay for Medicare for All. He says that many Americans would still come out ahead because they would no longer pay premiums or out-of-pocket bills for health care.

The new proposal was rolled out a day after Bloomberg reported that a polling firm associated with former Vice President Joe Biden had been studying which arguments against Medicare for All would be most effective with voters. One of its conclusions: the cost to taxpayers. Sanders responded to the news by insisting again that "no one earning less than $29,000 will pay any new taxes" under his plan, which he called "a great deal for the American people."

Massachusetts Sen. Elizabeth Warren has already unveiled plans to push for a similar wealth tax , which she often cites on the campaign trail -- to roaring approval from supporters -- as the potential source of funding for a series of ambitious programs. Sanders could be angling to establish a similar pitch, and respond to Biden, with a populist win-win proposal that pays for expensive new programs by soaking the rich.

Under Sanders' "tax on extreme wealth," married couples worth more than $32 million would pay a 1% tax on their wealth above that threshold. The rate would rise to 2% on net worth between $50 million and $250 million, climbing in increments to a 8% tax on wealth above $10 billion.

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