(CNN) Progressives and Republicans have found something in common amid the raging health care debate: They all love talking about single-payer insurance.

No, they haven't bridged any of the divides on health care policy, and a Canadian-style single-payer plan -- the left prefers to call it "Medicare for all" -- remains implausible in the current Congress.

But both sides are beginning to see a political benefit in bringing it up.

Progressives have long held universal health care as a marquee public policy goal and increasingly see opportunities to push for a radical overhaul as President Donald Trump and Republicans on Capitol Hill face headwinds in their efforts to roll back Obamacare.

Vermont Sen. Bernie Sanders, an independent, is readying a bill proposing a single-payer system, and is expected to file it once the Senate finishes considering the GOP effort to repeal and replace former President Barack Obama's signature law. And more Democratic senators are publicly endorsing such a system.

Last week, New York Sen. Kirsten Gillibrand, who began her career as a moderate "Blue Dog" member of the House, backed single-payer. Massachusetts Sen. Elizabeth Warren, meanwhile, told The Wall Street Journal, "now it's time for the next step. And the next step is single-payer."

For Republicans, the calculation is different, but simple: Obamacare is politically more popular than the legislation Republican leadership is pushing on Capitol Hill. The danger of undercutting many of its provisions, including barring insurance companies from rejecting customers or hiking rates due to pre-existing conditions, is clear. For senators from states that accepted and have benefited from Medicaid expansion under the law, the vote is even trickier.

But single-payer health insurance, or "Medicare for all," is a much more divisive proposition. A recent Pew Research Center poll found that while 52% of Democrats support it, that number drops to 33% when the field expands to include Republicans.

In the White House and on Capitol Hill, GOP officials are now floating the prospect of a single-payer future -- rather than the survival of Obamacare -- as the likely alternative to a successful repeal process.

"If we have to negotiate with Chuck Schumer and the Democrats, we're going to be looking down the barrel of a single-payer system because that's what they want to see happen," Sen. John Thune, R-South Dakota, said on "Fox News Sunday."

Trump's deputy press secretary Sarah Huckabee Sanders brought up single-payer health insurance -- without being asked -- at the White House press briefing on Thursday.

"The other bill out there that's gained the support of a majority of House Democrats is the Bernie Sanders single-payer plan that would cost the government $32 trillion over the next decades. One hundred and thirteen House Democrats, including the DNC vice chair, have signed on to this approach," she said, referring to Rep. Keith Ellison of Minnesota, the deputy chairman of the Democratic National Committee.

"The President believes that it's completely unaffordable and creates a one-size-fits-all government approach to health care," she said. "That bill and others like it on the other side that have been proposed are clearly deal-breakers."

Progressives are also seeking to make use of Obamacare's rising popularity -- and the threat of its undoing. After years spent criticizing the law from the left, they have rallied to protect it in the face of repeal.

"Right now the goal is defeat this terrible piece of (Republican) legislation and then regroup and go forward doing what every other major country on Earth does and (pass) Medicare for all," Sanders told CNN last week. Days earlier, he and organizers from MoveOn.org, the liberal advocacy group, were barnstorming Pennsylvania, Ohio and West Virginia, rallying opposition to the GOP bill.

But even as Sanders railed against Trump, tallied Obamacare's achievements and warned about the dangers facing those who might lose coverage, the mention of "Medicare for all" still triggered the heartiest outpouring of applause at already boisterous events.

"If Democrats retake power, the idea of a public option and Medicare for all are going to be a much easier sell because they stood shoulder-to-shoulder in the fight today," MoveOn's Washington director, Ben Wikler, said as protests swirled on Capitol Hill ahead of the July 4 recess.

The real test, though, will come when Sanders releases his new single-ayer bill later in the summer.

The 2011 edition had zero co-sponsors . This new legislation figures to arrive with more support from Democrats, including potential 2020 hopefuls like Gillibrand and Warren, and to greater fanfare from Republicans, who sense both opportunity and danger.

In both cases, the one sure bet is that both sides will be eager to chat about it.