WASHINGTON >> At first blush, many Americans like the idea of “Medicare for all,” the government-run health system that’s a rallying cry for Democratic presidential candidate Bernie Sanders.

But mention some of the trade-offs — from higher taxes to giving up employer coverage — and support starts to shrivel.

That’s the key insight from an Associated Press-GfK poll released Thursday. The survey also found that people’s initial impressions of Sanders’ single-payer plan are more favorable than their views of President Barack Obama’s health care overhaul.

A slim plurality of 39 percent supports replacing the private health insurance system with a single government-run, taxpayer-funded plan that would cover medical, dental, vision and long-term care, with 33 percent opposed. Only 26 percent say they support Obama’s hard-won health care law.

Yet it’s only like an air kiss for “Berniecare.”

Asked whether they would continue to support Sanders’ plan if their own taxes went up, under a third of initial supporters of the plan would keep backing it. About 4 out of 10 flipped to opposition.

About the same share of initial backers would ditch single-payer if it meant that people had to give up employer coverage. Twenty-eight percent would continue to support it.

Higher taxes and an end to employer coverage are both a given under the Sanders plan, which would replace private coverage with a taxpayer-funded program, while also offering more generous benefits such as no deductibles and no copayments, as well as coverage for long-term care.

“That’s pie in the sky,” said Patricia Combs, a retired junior-high math teacher from Springboro, Ohio. “It sounds really good, but I don’t think it’s attainable … people would complain about their taxes being raised.”

Elizabeth Medina of Chicago, an office manager not currently working, said she worries that quality would slip.

“Overall it sounds terrific,” she said. “Yeah! Let’s go for it! But Europe and Canada have their problems with the single-payer system … it’s subpar.”

Such second thoughts over far-reaching policy proposals are common, said Robert Blendon of the Harvard T.H. Chan School of Public Health, who tracks public opinion on health care.

For example, a “flat tax” may sound appealingly simple as millions of people assemble their W-2 forms, 1099s, and lately those new health insurance forms for the annual tax-filing ritual. But it gets tricky for flat-tax advocates when they have to decide which popular tax deductions to eliminate and which to keep.

“People say they believe in a principle, but when you describe the policy, it often loses support because they don’t like that there are side effects,” said Blendon.

The poll found increasing doubts about single-payer health care when other potential consequences are considered, such as slower availability of new drugs and treatments, and longer waits for non-emergency services.

Unlike higher taxes and having to give up employer coverage, those are not automatic consequences of converting to a government-run system. But such concerns would surely be raised as a President Sanders tried to lead the “political revolution” he promises.

The poll found that 51 percent of initial single-payer backers would switch to opposition if it took longer for new drugs and treatments to become available. Only 14 percent would continue to support the plan. Such an outcome could happen if drugmakers were required to prove that new medications are therapeutically superior to existing ones. The current standard is that new drugs be safe and effective.

Additionally, 47 percent of initial supporters would reconsider if “Medicare for all” meant longer wait times for non-emergency medical services. That could happen if budget-conscious administrators encouraged doctors and hospitals to be parsimonious in using high-tech imaging. Only 18 percent of poll respondents would continue to support the plan in that case.

Overall, the poll found that health care remains a top issue for Americans, with three-fourths calling it extremely crucial or very important. Health care ranked behind the economy but ahead of foreign policy concerns as well as domestic issues like income inequality.

Memo to those following the Republican presidential primary: Most people doubt that “Obamacare” will be repealed even if the GOP wins the White House.

Forty-nine percent say the Affordable Care Act will be kept in place with changes, whether major or minor. Another 6 percent say a Republican president will not be able to make any changes to Obama’s law.

“A lot of people who couldn’t have health care before now have health care, so I don’t think you are going to be able to just turn around and strip all those people of their health care,” said Lillian Duren, a recently retired psychiatric emergency nurse from Brooklyn, New York. “You need to fix what doesn’t work and keep moving.”

The Republican presidential candidates have promised to repeal the health law, but they haven’t detailed how they would replace it.

The AP-GfK Poll of 1,033 adults was conducted online Feb. 11-15, using a sample drawn from GfK’s probability-based KnowledgePanel, which is designed to be representative of the U.S. population. The margin of sampling error for all respondents is plus or minus 3.4 percentage points.

Respondents were first selected randomly using telephone or mail survey methods, and later interviewed online. People selected for KnowledgePanel who didn’t otherwise have access to the Internet were provided access at no cost to them.

Online: ap-gfkpoll.com