ABORTION AND SPOUSAL NOTIFICATION: As several people point out, that's going to be an issue with regard to Alito. I'm not sure what I think about this issue, but looking at the Pennsylvania statute I notice a lot of exceptions, one of which is this: "Her spouse is not the father of the child."
I'm not sure about Pennsylvania, but in many states her spouse -- even if he's not the father of the child -- would still be on the hook for child support. Likewise, if he didn't want children, but she disagreed, lied to him about birth control, and got pregnant. And he certainly couldn't force her to have an abortion if she did so, even if his desire not to have children was powerful, and explicitly expressed at the outset. (The usual response -- "he made his choice when he had sex without a condom" -- never comes up in discussions of women and abortion.)
So where's the husband's procreational autonomy? Did he give it up by getting married? And, if he did, is it unthinkable that when they get married women might give some of their autonomy up, too?
The problem here is that you can say "my body, my choice" -- but when you say, "my body, my choice but our responsibility," well, it loses some of its punch.