It's hard to say:
Many Americans probably don't understand the healthcare bill as well as many in the media might assume. Only 51% of adults in an April 2012 Kaiser poll responded that they had enough information to understand how the law would impact them personally. A March CBS poll gave pretty much the same result. How can Americans judge a healthcare law that will make a difference in lives, if they don't comprehend how it will?
Even when you broaden it out to the healthcare law as whole (without taking into account its personal impact), only 18% of Americans in a Pew poll felt they understood the law very well, while 31% said not too well or not very well at all. Who is to say, then, that Americans' opinions wouldn't change were they to gain a better grasp of what the law entails?
Jonathan Bernstein seconds this argument.