At a prostate cancer survivors breakfast last week, former Secretary of State Colin Powell, a Republican, marveled at the quality of single-payer health care systems abroad and suggested the U.S. follow suit.

Amid frustration with the rollout of President Barack Obama's health care plan, some members of Congress who agree with Powell are pushing for consideration of such a system.

Sen. Bernie Sanders, I-Vt., introduced the American Health Security Act of 2013 on Monday, which would require states to create their own single-payer insurance systems. A House version was introduced in March by Rep. Jim McDermott, D-Wash.

In single-payer systems, the government pays for most non-elective medical care. Supporters say adopting that tax-financed model would improve care and dramatically reduce costs by eliminating overhead and insurance company profits. Opponents fear rationing and reduced personal choice.

The 2010 Affordable Care Act, commonly known as Obamacare, retained the private health insurance industry and forces Americans to buy private insurance policies or face a fine. Attempts to include a public health insurance option were blocked by Republicans and conservative Democrats who feared it would be a backdoor to a single-payer system.

Powell said, however, that he would welcome the adoption of a socialized insurance system.

"I don't see why we can't do what Europe is doing, what Canada is doing, what Korea is doing, what all these other places are doing," Powell said at the Dec. 5 event. "I am not an expert in health care, or Obamacare, or the Affordable Care Act, or however you choose to describe it, but I do know this: I have benefited from that kind of universal health care in my 55 years of public life."

The retired four-star general pointed to his military health insurance as an example of high-quality government insurance and shared an anecdote regarding his firewood supplier -- a woman named Anne -- who sought help paying for an MRI scan not covered by her private insurance policy.

"Every country I've visited, every developed country, they have universal health care ... I think universal health care is one of the things we should really be focused on," Powell said. "Whether it's Obamacare, or son of Obamacare, I don't care. As long as we get it done."

Powell's remarks were reported Monday by ABC News, which cited a report in the Puget Sound Business Journal.

Although widely regarded as a possible GOP presidential candidate in the 1990s, Powell drifted from party orthodoxy during President George W. Bush's second term, growing increasingly skeptical about the Iraq War. He endorsed Obama in 2008 and 2012.

Rep. Rush Holt, D-N.J., sees Powell's endorsement of single-payer systems as a sign Americans will embrace the idea "sooner rather than later."

"It's not a foreign idea," he said, pointing to millions of Americans with Medicare, Medicaid and military-provided health insurance.

Holt is an enthusiastic supporter of the Expanded & Improved Medicare For All Act proposed by Rep. John Conyers, D-Mich. The bill has been introduced annually since 2003 and would finance public health insurance for all Americans with a payroll tax. Holt also supports Obama's health care overhaul, but feels it should be considered a first step.

"If insurance companies began to talk about how much they are benefiting from the Affordable Care Act there might be a reaction against it," Holt told U.S. News. "Insurance companies do benefit from millions of new customers and insurance companies still are not giving the full benefit for premium dollar that they could."

Holt cautioned that any successful push for a single-payer system would require presidential leadership. At the moment, he added, opponents of the 2010 law have successfully "shifted the debate to just trying to implement the Affordable Care Act at all, rather than having the discussion shift to how to ... set the stage to move on to the best possible system."

Sanders, an independent who caucuses with the Democrats, is trying to channel frustration with the law's rollout, which he says is actually making Americans more sympathetic to single-payer systems.

"As the president fully understands, the rollout has been a disaster, the website has been a disaster," he told The Daily Beast. "When you have a lot of complications, it is an opportunity for insurance companies and drug companies and medical equipment suppliers to make billions and billions of profits rather than to see our money go into health care and making people well."

In Vermont, the state government is prepared to roll out its own single-payer system if the U.S. Department of Health and Human Services approves the use of federal funds to do so.

Polls show a sizable minority of Affordable Care Act opponents believe the law doesn't go far enough. Polling on a single-payer model itself varies widely. A 2009 CBS News/New York Times poll pegged support for single-payer health insurance at 59 percent, but a March 2013 Rasmussen poll found just 38 percent support.