Generally, demographic groups align with their traditional party affiliations. Women, minorities, singles and young voters are the most likely to support the legislation (and the Democratic Party), while the elderly, men, whites and married individuals are more likely to object to the legislation (and support Republicans.)

But Americans are split on what they'd like their legislators to do about the law. Around three in 10 say they want full repeal, while two in 10 say only certain parts of the law should go. A quarter of Americans say Congress should further expand healthcare coverage, while 13 percent say the legislature should stop now.

It's also not clear how the court's decision could affect the calculus for November. While four out of every five Americans say healthcare will have some impact on which candidate they choose, only two in 10 say it will be their sole consideration. 

The survey also found that Americans considered the Supreme Court's decision a political one, despite Chief Justice John Roberts bucking expectations and siding with the liberal wing. Almost two-thirds of those surveyed said politics played a major role in the decision.