(CNN) A key plank of Vermont Sen. Bernie Sanders' presidential campaign platform is his proposal to have the US adopt a "Medicare for All" government health insurance system.

Under the Sanders proposal, private health insurance companies would be eliminated . Every resident would be covered by a single government insurance program that would pay the entire cost of almost every health care service and product, from routine checkups to major surgery to prescription drugs to dentistry to treatment for mental illness.

ABC host George Stephanopoulos challenged Sanders over his proposal on Sunday. Stephanopoulos mentioned a January poll by the Kaiser Family Foundation that found that support for "Medicare for All" dropped sharply, from 56% to 37%, when people were told it would eliminate private health insurance companies.

Sanders responded that his plan gets more popular when people are told of its benefits, including that it would expand coverage to include dental care and hearing aids and would eliminate premiums, copayments and deductibles. "For the overwhelming majority of people," Sanders continued, "health care will be much less expensive."

"And by the way: Medicare today is the most popular health insurance program in the country. Private health insurance is not particularly popular," he said.

This was a slight but important change from what he had said at the Democratic debate on Thursday night. On Thursday, he said , "Medicare is the most popular health insurance program in the country. People don't like their private insurance companies, they like their doctors and hospitals. Under our plan, people go to any doctor they want, any hospital they want."

At the debate, he spoke of the popularity of insurance companies. On ABC, he spoke of the popularity of private health insurance itself.

For the moment, we'll ignore the claims that health care will be much less expensive under Sanders' plan and that people could go to any doctor or hospital they want. Let's delve into his claim about the respective popularity of Medicare and private health insurance.

Facts First: Sanders is correct about the popularity of Medicare: It is popular across political lines, and it is more popular than private insurance. Private insurance, though, is also quite popular with the people who use it -- even though insurance companies are not.

Medicare is popular

There is no doubt that Medicare, the government insurance program for people 65 and older and for younger people who have disabilities, is highly popular. That popularity extends across party lines. In one Kaiser Family Foundation poll in 2017, 85% of Democrats, 74% of Republicans and 83% of independents said they held a favorable view of the program.

The available data suggests Medicare is indeed likely the most popular insurance program in the country. Medicaid, the government insurance program for low-income people, is also popular, but somewhat less than Medicare, said Liz Hamel, director of public opinion and survey research for the Kaiser Family Foundation. In a 2015 Kaiser poll , for example, 75% of people covered by Medicare said it was working well, versus 65% of people covered by Medicaid. And private health insurance does worse than Medicare in various kinds of surveys.

"It is accurate. Medicare is more popular," said Robert Blendon , professor of health policy and political analysis at Harvard's schools of public health and government.

But, as Blendon pointed out, being less popular than something that is highly popular doesn't mean private insurance is unpopular.

Private insurance is also popular

We can't say Sanders' claim about private insurance is flat false. What constitutes "not particularly popular" is subjective, and there is some data to support his argument. However, there is other data that significantly weakens the argument.

If you ask people for their views on the cost of their health care, people on Medicare are much more likely to be satisfied than people on private insurance. In a Gallup poll in 2018, 51% of people on private insurance said they were satisfied with the total cost they paid. That was much lower than the 70% of satisfied people on Medicare or Medicaid.

If you ask people for their views on health insurance corporations , they tend to be negative. In a 2015 poll by the Kaiser Family Foundation, 44% said they had a favorable view of these companies, while 51% said they had an unfavorable view.

Sanders can point to figures like these to bolster his case.

But the story changes when you ask people for their views on their own private insurance plans rather than about insurance companies or costs. In poll after poll, for years, Americans using such plans have expressed positive opinions.

"Americans rate the quality of their health care and coverage through private health insurance highly," said Jonathan Oberlander , professor and chair of social medicine at the University of North Carolina at Chapel Hill.

"On the question of costs of coverage, I would say Sen. Sanders' statement is accurate. However, in terms of how Americans with private insurance rate their overall coverage and quality of care, it is inaccurate."

More than 155 million Americans received private coverage through employers in 2017, or about 58% of people under age 65.

Last year, the Kaiser Family Foundation asked people who have employer plans to give their coverage a grade. Twenty-five percent gave it an "A," or excellent; 43% said "B," or good. These results -- about two-thirds rating their employer coverage positively -- have been quite consistent dating back to 1997, according to data provided to CNN by Kaiser.

In a Gallup poll last year, 85% of people who used private insurance said the quality of their health care was "excellent" or "good," versus 79% of people on Medicare or Medicaid. (Gallup combined the Medicare and Medicaid groups in its report on the poll.) When people were asked about their coverage itself rather than the quality of care, 79% of people on Medicare or Medicaid said it was excellent or good, versus 70% of people on private insurance.

So the government programs won on the issue of coverage, but private insurance still did well.

In 2015, Gallup asked people if they were satisfied with the way the health care system works for them. Seventy-seven percent of people on Medicare said they were satisfied. So did 69% of people on insurance from current or former employers. Once again, Medicare did better, but there was clear evidence that most people with employer coverage were also content.

A Sanders campaign aide pointed out that uninsured people are left out of survey questions that ask people who already have private insurance how they feel. Therefore, the aide said, it is quite possible that the overall public view of private insurance is less positive than these results show.

That is a valid point. But when discussing the popularity of private insurance, it's at least worth mentioning, as Sanders did not, that private plans tend to be popular with the people covered by them.

This story has been updated.