The great conflation continues. Might Americans support access to abortion? Perhaps. Might they support tipping a perfectly viable fetus from the womb or killing it after birth. No, not on our most evil day.
IMO there is not enough discussion on that side of it.
I suppose some states might just say “no abortion” at all, but I don’t think that will be very common. What I do expect is a lot of restriction about partial birth abortion, late term abortion, and other things. Politically, a total ban is hard. But getting rid of the most distasteful aspects of this is comparatively easy. I expect that sensible restrictions will become common.