I should clarify my earlier post on abortion, which I think I wrote too hastily. First of all, on how Democrats used the filibuster: they didn't use it to filibuster Supreme Court nominees, but conservative judges who would have been successful supreme court nominees had they ended up on the Court of Appeals. My take is that this meant a less conservative court than would have existed by the end of the Bush years; your mileage may vary. It also means there are fewer lower circuits on which abortion opponents are likely to successfully press their quest.
Second, Kevin questions whether keeping Roe intact is really a minority view. It depends on how you define it. Roe polls well. But the things that Roe has prevented legislatures from doing--like making abortion illegal in the second trimester--don't. Even polls that show fairly strong support for Roe also show that most people think abortion should be illegal except in cases of rape or incest, when the mother's physical health is in danger, and when the fetus is severely deformed.
So if the challenge were a South Dakota style flat ban for all reasons, then yes, that would be unpopular. But if the challenge were a law that outlawed second trimester abortions except in the abovementioned four cases, it would be fairly popular.