President Donald Trump called Sen. Bernie Sanders' proposed plan to eventually have Medicare cover the health-care needs of all Americans "a curse on the U.S." that he promised to veto, if need be.

But Trump also noted that he had earlier warned his fellow Republicans in Congress that they would face the threat of such a single-payer health plan if they did not quickly repeal Obamacare.

Trump's broadsides came in two tweets the president posted Thursday, a day after Sanders, a Vermont independent, rolled out his "Medicare for All" plan.

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Sanders responded to the Twitter post during a radio interview: "Where can we begin on that? We kind of tweeted right back and our tweet said something to the effect, 'Mr. President, let me tell you what a curse on the American people is and that is your support for legislation that would throw 23 million people off of the health care they currently have and then provide huge tax breaks for the rich and large corporations.'"

"Providing health care to every man, woman and child in this country, that's not a curse. That's what every other major country on earth does, and that's what we should be doing," the senator said, according to a transcript of the interview provided by "The Michelangelo Signorile Show" on SiriusXM Progress.

Despite the fact that Sanders has been joined by 16 Democratic senators as co-sponsors of the bill, there is effectively no chance that Trump will be forced to follow through on his vow to veto the legislation anytime soon.

Republicans hold a two-seat majority in the Senate, and a 46-seat majority in the House of Representatives. The GOP thus has the power to thwart passage of Sanders' bill.

That legislation seeks to put the United States on the same footing as other major industrialized countries, whose governments directly fund the health-care needs of their citizens.

Tens of millions of people in the U.S. get such coverage via Medicare, for mainly senior citizens, and Medicaid, which serves poor people.

But millions more get health coverage through a job or a privately purchased insurance plan.

And 28.1 million Americans lacked any health insurance coverage as of last year, according to the U.S. Census Bureau.

Despite its current long odds of passage, the support Sanders has garnered from leading Democrats for his bill underscores how significantly the health-care debate has shifted since Trump was elected president last fall.

Trump and Republicans in Congress had planned for a quick repeal of major parts of Obamacare, and for passage of new health-care legislation that would have dramatically scaled back federal support for customers of individual health plans.

But their expectations were dashed over the summer as GOP leaders were unable to get the 50 Republican senators required to pass such the legislation with Vice President Mike Pence's tiebreaking vote.

At the same time, a growing number of Americans have said they support the idea of a single-payer health system.

A national survey by the Pew Research Center released in July found that 60 percent of people believed the federal government "has the responsibility to ensure health coverage for all."

Among those people, 33 percent say that the government should have a single-payer program to meet that responsibility, as opposed to using a mix of government and private programs. Obamacare uses such a mix of programs to expand health coverage.

That level of support for single payer is up from 28 percent in January, and up from just 21 percent in March 2014.

Pew also found that 85 percent of Democrats believed the government has a responsibility for making sure all Americans have health coverage, up from 69 percent in March 2014.

Among Republicans, 30 percent said the government has such a responsibility. That is down 2 percentage points since January, but is still 12 percentage points higher than the level of support among Republicans in March 2014.