Ancient history now, I suppose, like so many things, but I think the
Terri/Michael Schiavo case is instructive about the abortion question, generally. I'm too lazy to hunt up the precise polling at the time, but a lot of people thought Michael Schiavo was the villain, that he was trying to do the wrong thing, and sided with the Schindlers (her parents). Then the legal process in Florida played out - a very long legal process - and the courts ultimately sided with Michael. Right decision by him, wrong decision, maybe reasonable people can disagree (I'm not interested in arguing it), though that's separate from the issue of
who had the power/right to decide.
And then Congress stepped in. Tom DeLay stepped in. And everyone all over the country could imagine the Bug Man interfering in their lives at the worst most difficult moments. It's one thing to disapprove of Michael, quite another to imagine your medical and end of life decisions being hijacked by the freaks in Congress after the normal (which was hardly normal) process had played out.
Plenty of people disapprove of abortion in a general sense, but not as many really want the reality of a post-Roe world. Horror stories will be there daily, if anyone chooses to report on them, and one political party had better get out in front of it.