I can sympathize with the arguments made by anti-choicers, but regardless of how firmly they believe whatever they believe, it doesn't change the FACT that when abortion was illegal, it happened anyway, and a lot of people died seeking back-alley abortions.
You cannot stop abortions from happening, even if you desperately want to. The question becomes, does a woman have a right to do something to her own body without government interference. It's a recognized right of privacy that is protected by the Constitution.
Now, there may be some merit to how it happens, who is notified, etc... (I don't think so, others might), but whether a fetus is a baby or not is an irrelevant question. Even if a fetus was a grandmother, it doesn't change the fact that the mother can abort it. Even if abortion were illegal again.