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.

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.