Abortion hypothetical

Here's an interesting topic, at Patterico's blog:

Suppose the technology existed to safely remove a fetus from a womb at any gestational stage for incubation elsewhere until birth. If such "no-death abortion" was available to any woman who wanted it, would most abortion rights supporters stand down?

I'm especially interested in what abortion rights supporters have to say, because I've always thought that their position is based on opposition to forced pregnancy ("Keep your laws off my body").

Patterico mentioned having raised a similar question to a couple of women, one pro-choice, another pro-life.  The pro-choice woman absolutely did not accept the "no-kill abortion" described above.