WASHINGTON -- The last thing House progressives want is for the Supreme Court to strike down President Barack Obama's health care law. But if the high court rules Thursday that some or all of the law is unconstitutional, progressives are ready to renew their push for the model of health care they wanted all along: the single-payer option.

"It's easy to see it's a good idea," Rep. Keith Ellison (D-Minn.), co-chairman of the Congressional Progressive Caucus, told The Huffington Post. "It's the cheapest way to cover everybody."

Ellison said all 75 members of the caucus have already signed onto a bill by Rep. John Conyers (D-Mich.) to create a single-payer, publicly financed, privately delivered universal health care program. The proposal would essentially build on and expand Medicare, under which all Americans would be guaranteed access to health care regardless of an ability to pay or pre-existing health conditions.

House progressives pushed hard for a single-payer option, such as the "Medicare for all" approach, during the health care reform debate in 2009. But House Democratic leaders couldn't come up with the votes to pass the proposal, and progressives ultimately caved on the idea in order to pass the president's plan, on the reasoning that some reform was better than none at all.

Asked why progressives think a single-payer option could advance this time around, Ellison said if the Supreme Court strikes down some or all of the existing health care law, it shows that the individual mandate at the heart of the law -- a concept originally backed by conservatives -- was a failed approach.

"We've tried it the right-wing way. Let's try it the right way," he said.

Rep. Jerrold Nadler (D-N.Y.) said he led the charge for reviving the single-payer health plan during a recent Progressive Caucus meeting.

"We agreed we're going to come out in favor of Medicare for all, in both instances," he said, referring to the Supreme Court possibly striking either some or all of the health care law. "One disadvantage of saying, 'Let's go for single payer,' is that by and large the American people have no idea what that means. But the advantage of saying 'Medicare for all,' the American people do know what that means. And it's a very popular proposal."

Nadler said he didn't know how Democratic leadership would feel about revisiting the idea. He said that will depend largely on how the White House responds to the Supreme Court's ruling, whatever it is.

A House Democratic leadership aide suggested party leaders aren't about to embrace a single-payer option anytime soon.

"I think we have to recognize the situation we're in with House Republicans, where we can't even get bipartisan legislation finished," said the aide. "We can talk about specific proposals and have discussions and have that as something to focus on or talk to constituents about as they run for reelection. It's just not going anywhere in this Congress."

UPDATE: 1:45 p.m. -- White House Press Secretary Jay Carney later brushed off a question about whether Obama would support a single-payer option in the event his law gets struck down.

"The president favors the Affordable Care Act," Carney said at his daily briefing. "The president, as you are, is awaiting the decision. We will assess it as it comes."

UPDATE: 2:55 p.m. -- Progressives acknowledge there are obstacles but say it would still be best to embrace a "Medicare for all" approach.

"There's no chance that [House Speaker] John Boehner is going to bring that up for a vote," Rep. Peter Welch (D-Vt.) said on a conference call. "We have to have an alternative policy that we're promoting that shows where we want to go," he said, adding that he sees it as a long-term fight that could have short-term benefits in the fall.

"We'll have to start agitating and the two focuses for me will be what we're for -- Medicare for all -- and no. 2, indicting a Boehner-led House that has no Plan A, even to maintain the popular insurance reforms that mean a lot to the American people," he said. "It will be an opportunity for the American people to weigh in, in the election."

CORRECTION: A previous version of this article misidentified Keith Ellison as a representative from Missouri. He is from Minnesota.

Below, a slideshow of previous health care reform efforts:

PHOTO GALLERY Health Care Reform Efforts In U.S. History