I think most Americans really don't care about abortion. At least not enough to get involved in any way. So they try to settle on something that sounds least offensive, which is the compromise you are talking about.
But it's doomed to failure, because the compromise makes no sense. If the anti-abortion activists are right, then abortion needs to be banned. If the abortion rights activists are right, then abortion decisions need to be left to the woman. Saying that abortion is okay up to a point, and not okay after that, has no logical underpinning. As evidence, we have the impending toppling of Roe, which fundamentally assumed that such a point must exist, and that this point was the point around which to balance the various interests and find that elusive compromise.
What's the most common opinion people you know have about abortion? I've never done a survey, but I can answer easily: "I don't agree with it, but it's ultimately up to the woman." Almost everyone I know would agree with a statement like that. But the statement makes no sense. Rephrase that a bit, and it says, "I don't agree with murder, but it's ultimately up to the murderer."
Anyway, what I'm really saying is the "common sense" approach to abortion lacks any actual sense, and that's why it's doomed. Someone will win. I suspect it will be the anti-abortion activists who eventually come out on top.