While Democrats are nearly united (85 percent) in saying it's the GOP's fault if the ACA collapses, Republican voters are more divided. Fifty-six percent say any future blame should be assigned to Obama and his party, but a third are willing to blame Trump.

Perhaps most ominously for Trump, 65 percent of independents say he's on the hook for America's health care system now.

Trump, whose own statements on health care frequently fluctuate, has hinted publicly on a number of occasions that Republicans would be better off not trying to come up with an alternative to the ACA for which they would be blamed. Indeed, after backing a replacement bill that Republicans failed to get through Congress, Trump reassured supporters by saying that they simply had to wait until the collapse of the ACA marketplace.

Democrats are worried that Trump and Congressional Republicans will do everything in their power to make the president's prediction come true, including by stoking fears among insurers that participating in the ACA is not worth the risk or by dropping enforcement of the individual mandate.

Some recent actions by Republicans indicate they are wary of appearing to undermine the ACA. Both Congressional leaders and the Trump administration have announced support for continuing payments to insurers that allow marketplace health plans to offer discounted prices to low-income customers.