Elizabeth Warren released her sweeping plan to overhaul the US healthcare system on Friday, proposing $20.5tn in federal spending over the next decade to provide healthcare to every American without raising taxes on the middle class.

Warren estimated the money could be generated through a combination of, among other things, higher levies on capital gains and other investments and new taxes on the wealthiest 1% of Americans.

In a lengthy online post, Warren said a cornerstone of her plan would require employers to transfer to the government almost all the $8.8tn she estimates they would otherwise spend on private insurance for employees.

“We can generate almost half of what we need to cover Medicare for All just by asking employers to pay slightly less than what they are projected to pay today, and through existing taxes,” she wrote.

The details Warren’s Medicare for All plan aim to quell criticism that the presidential candidate has been vague about how she would pay for her ambitious proposal. Warren has also been repeatedly targeted on the Democratic debate stage over whether the plan would include middle-class tax hikes.

While progressive activists praised the release, Warren faced a swift blowback from her moderate Democratic rivals, most prominently Joe Biden, whose campaign said it amounted to “mathematical gymnastics”.

“She’s making it up,” Biden told PBS NewsHour when asked about the estimated costs for the plan. “Nobody thinks it’s $20 trillion. It’s between $30 and $40 trillion.”

“Look, we don’t have to go that route,” the former vice-president added. “All we have to do is go back, restore Obamacare, provide a public option.”

Warren defended herself against the attacks by emphasizing that the cost and revenue projections outlined in the plan were authenticated by former senior Obama administration officials. She said: “So if Joe Biden doesn’t like that, I’m just not sure where he’s going.”

How would the plan work?

Elizabeth Warren speaks during an event to introduce the Medicare for All Act of 2017 on Capitol Hill. Photograph: Yuri Gripas/Reuters

Companies with fewer than 50 employees that don’t already sponsor coverage would be exempted from the proposal. And in a nod to unions, whose support will be key in the Democratic primary, Warren said employers already offering health benefits under collective bargaining agreements would be allowed to reduce how much they send to the federal government – provided they pass those savings on to employees.

Democrats have spent decades debating the proper role of government in healthcare, and the complicated politics surrounding the issue quickly resurfaced. Other Democratic candidates, including Biden, have attacked Medicare for All as too dramatic of an overhaul. Donald Trump has branded it socialism.

But Warren and Bernie Sanders, who has been the chief architect of the idea of Medicare for All, have replied that a dramatic overhaul is exactly what the system needs.

Then there’s the task of passing such legislation through Congress. A Republican-controlled Senate is unlikely to approve anything approaching Medicare for All. And if Democrats took the Senate majority, the party almost surely wouldn’t have enough votes to break a filibuster.

“There’s the practical application of getting 60 people in the Senate who are going to vote for this,” said the former Iowa governor Tom Vilsack, who has worked with Warren on rural policy.

A critical question for Warren is whether her $20tn cost estimate is accurate. Some independent experts have raised doubts; the Urban Institute thinktank recently pegged the cost closer to $34tn over 10 years.

“They are making more aggressive assumptions about the same things we already made aggressive assumptions about,” said John Holahan, an economist at the Urban Institute who co-authored a recent cost analysis that the Warren campaign is using as a starting point for its estimates.

The Emory University economist Ken Thorpe, who has done his own estimates of Medicare for All, said: “This seems like an exercise to low-ball the revenues needed to actually make this enormous transition.”

If Warren is underestimating the cost by that much, her predictions about needed tax revenue would come up well short.

If the transfers from private businesses to the government don’t raise enough money, Warren says she would make up the difference by imposing a supplemental contribution requirement for big companies “with extremely high executive compensation and stock buyback rates”.

And a whopping $2.3tn would come from stronger enforcement of existing tax laws – money that would have to be identified and collected before it could be used.

Over the weekend, Warren and more than a dozen other candidates will be in Iowa, which will in three months hold the nation’s first presidential caucuses. Healthcare remains a dominant issue.

A new Iowa poll released on Friday found Warren leading a tight race in the state, while Biden has fallen. The New York Times-Siena College poll found the Massachusetts senator attracted the support of 22% of the state’s Democratic voters, with Bernie Sanders a close second at 19% and Pete Buttigieg just behind him at 18%. Biden narrowly comes in fourth at 17%.