The only problem with this is that we don't really know or even have the slightest idea what would happen (even though this will never happen). The issue could become irrelevant, as people realize that THE PRESIDENT DOESN'T REALLY HAVE THE POWER TO OVERTURN OR STOP ROE v. WADE FROM BEING OVERTURNED.
Perhaps because the President has the power to nominate judges and justices, and as long as Roe vs. Wade (and Planned Parenthood vs. Casey, by extension) remains established law it will remain a federal issue.
Personally I agree that there could very well be a backlash -primarily against the Republican Party (the one major political party that prides itself on being 'pro-life'). Obama could face some blowback as well for appointing Sotomayor, but I have my doubts -he could simply state that he was as misled as then-President George H. W. Bush was.
In the interim this could lead to Democrats regaining lost ground in 2012 from the 2010 midterm election, but then overreaching on the issue by attempting to pass some variant of the Freedom of Choice bill, leading to a Republican revival in the 2014 and 2016 elections.
I'd have to agree with you completely on that last paragraph.