WASHINGTON (AP) — A new poll finds that many Americans like the idea of "Medicare for all," the government-run health system espoused by Democratic presidential candidate Bernie Sanders.

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

That's the key insight from an AP-GfK poll released Thursday.

A slim plurality of 39 percent supports replacing the private health insurance system with a Sanders-like government-run, taxpayer-funded plan that would cover medical, dental, vision and long-term care.

But asked whether they would continue to support Sanders' plan if their own taxes went up, about 3 in 10 of the initial supporters would keep backing it. Four out of 10 flip to opposition.

(Story by: Ricardo Alonso-Zaldivar, Emily Swanson, The Associated Press)