Medical students and residents during daily rounds at Our Lady of the Lake Regional Medical Center in Baton Rouge, Louisiana, in 2015. Gerald Herbert/AP Images Once confined to the fringes of debate, the idea of single-payer healthcare is making a comeback with support from some unlikely places.

Single-payer healthcare is a system used in Canada, France, the UK, Australia, and other countries that in theory provides nearly universal coverage through the government rather than private insurance companies. (Some countries use a hybrid public/private structure.)

While progressive groups have long pushed for a single-payer system in the US, Democratic Party leaders are starting to suggest they are open to advocating such a system.

"We're going to look at broader things" for the nation's healthcare system, Senate Minority Leader Chuck Schumer said on ABC on Sunday. "Single-payer is one of them."

Some of the richest and most powerful Americans — many of them Republicans — have recently brought up the possibility of shifting to a single-payer system. It comes as the Republican-controlled government has spent months attempting to revamp the US healthcare system with legislation that would move the system further from single-payer.

Perhaps most striking was Aetna CEO Mark Bertolini recently saying at a private conference that the US should start considering the idea.

According to Vox's Sarah Kliff, Bertolini told Aetna employees at a town-hall-style meeting in May that he thought "we should have that debate" about single-payer "as a nation."

Kliff said that based on his comments, Bertolini did not support a total government-run single-payer system but could be open to a private-public system used in some nations.

"So the industry has always been the back room for government," Bertolini said. "If the government wants to pay all the bills, and employers want to stop offering coverage, and we can be there in a public private partnership to do the work we do today with Medicare, and with Medicaid at every state level, we run the Medicaid programs for them, then let's have that conversation."

The idea, for Bertolini, is that the government would finance insurers to provide the care, similar to Medicare for all. The Aetna CEO, however, said he didn't think total government-run healthcare was the solution, which makes sense, considering it would put him out of business.

"But if we want to turn it all over to the government to run, is the government really the right place to run all this stuff?" Bertolini said. "And that's the debate that needs to be had. They could finance it, and if there is one financer, and you could call that single-payer."

The shift is understandable for Aetna, since for the first time, most of its business is coming from government programs like Medicare and Medicaid. Additionally, as Bertolini likes to point out in interviews, the insurer was the first Medicare provider in 1965.

In addition to backing from the CEO of one of the five largest public insurers in the US, the single-payer idea has also received recent support from the business titans Warren Buffett and Charlie Munger.

Munger, a Republican, railed against the current US healthcare system at Berkshire's annual meeting on May 6 and in subsequent interviews said the country should shift to single-payer.

"The whole system is cockamamie," Munger said in an interview with CNBC's Becky Quick in May. "It's almost ridiculous in its complexity, and it's steadily increasing cost, and Warren is absolutely right. It gives our companies a big disadvantage in competing with other manufacturers. They've got single-payer medicine, and we're paying it out of the company."

When asked by Quick if he supported single-payer, Buffett said, "I personally do."

Buffett also bemoaned the fact that healthcare costs make up roughly 17% of the US's gross domestic product — according to the Centers for Medicare and Medicaid Services, it was 17.8% of GDP in 2015 — much more than any other developed nation. The Berkshire CEO said these increased costs for businesses, rather than the corporate tax rate, were holding back American competitiveness.

Even President Donald Trump, who has supported Republican-led efforts to overhaul the healthcare system, has praised Australia's public-private system in a meeting with Prime Minister Malcolm Turnbull and in subsequent tweets.

"I shouldn't say this to our great gentleman and my friend from Australia, because you have better healthcare than we do," Trump said in his meeting with Turnbull on May 5.

After critics noted that Australia has a universal healthcare system in which the government pays roughly 70% of all costs, Trump used Twitter to defend the comment the next day.

"Of course the Australians have better healthcare than we do — everybody does," Trump tweeted.

With Republican control of the presidency and Congress, much of the talk about single-payer is likely to amount to just talk on the national level. There is some action on the state level, though — both California and Illinois have recently discussed legislation that would provide a single-payer system, and others have previously discussed the issue.