Mike,
I am basically a pro-choice advocate, which contrary to popular belief, is not the same as pro-abortion.
There are those people who feel strongly against abortion and have stated they will not rest until ALL abortions are made illegal. But it doesn't just stop with that medical procedure because these individuals are also against things like the "morning after" pill and any forms of contraception to prevent pregnancy in the first place.
Given that sort of opposition to abortion, it could be that pro-choice advocates will fight any attempts to infringe upon this right from any angle, out of a fear that if they begin to lose these exceptional cases, then over time, that basic right will be completely eroded and overturned. This is simply my opinion and I have nothing to base this on.
I personally have issues with partial birth abortions, but as a man, I don't feel it is my place on to tell a woman what she can, or cannot do, with her body.