Scott Lemieux doesn't think so:
The conventional wisdom would suggest that supporting reproductive rights is, on net, a national net negative for the Democrats. I see little basis for this belief. The consistent two-for-one public support for Roe v. Wade certainly puts the burden of proof on those who argue that abortion is a net loser for the Democrats in presidential politics.
Moreover, contrary to the assumption of many pundits, affluent, educated voters (who are relatively more socially liberal) generally place a higher priority on social issues than working-class voters do. To give another example, claims that same-sex marriage swung the 2004 election for George W. Bush turned out to be empirically wrong. Again, too many pundits focused on the opponents of same-sex marriage that referenda might have mobilized, while ignoring the affluent suburban voters who were alienated by Republican demagoguery on the issue.