Noam Scheiber sees real room for movement: 

Had Anthony Kennedy been the deciding vote, the conventional wisdom would have been that this was a partisan decision with an unreliable and unpredictable swing-voter more or less arbitrarily siding with the liberals. But with the Court’s conservative chief justice providing the fifth vote, the decision has real heft. Not only is this likely to grab the attention of voters who had no opinion beforehand (though opinion-formation is simply beyond the capacity of some of them), it’s likely to get the attention of the fraction of health care opponents who told pollsters they wouldn’t necessarily be upset if the court affirmed the decision. And that could be a very big deal for the political legitimacy of the health care law going forward.    

Tom Jacobs cites recent research on Roe v. Wade

Analyzing public opinion data from the era, [John] Hanley and his colleagues report that “among those who had heard of the decision, we see that support for abortion increased in nearly every one of the demographic groups studied” between 1972 and 1973. They add that “for all groups considered except infrequent church attenders” (who presumably were more pro-choice to begin with), “the effect of the decision appears to have been higher levels of permissiveness toward abortion.” The researchers add that “Whether this short-run effect can be maintained is another question altogether,” noting that the Roe v. Wade decision “did catalyze an organized response among activists that produced sharp conflict over abortion rights in the late 1970s, and up to the present day.”So the health-care decision won’t end the debate. But it may boost support for the plan over the coming months, which gives the Obama re-election campaign another reason to feel good about the result.