I mean I'm not an American so I'm not the one to answer that question. Although I think that the length of time that its been a touchstone issue for as many people as it has plus the heated rhetoric around it, that seems rather unlikely. Plus also: what compromise would be appropriate? The law in Great Britain (not Northern Ireland - abortion is still illegal there although the ECHR has ruled that is incompatible with the European Convention on Human Rights) is that abortion is legal until 24 weeks provided that a woman can convince two doctors that the procedure is needed - its the latter bit that is a lot more restrictive than the American law since its not truly abortion on demand, but considering that the BMA have recently voted to support totally decriminalising abortion before that point that is probably not the barrier that it sounds to most people. Sure that's one of the more liberal laws in Europe and you could look at some of the other ones but I doubt that would be restrictive enough to most people on the other side of the issue.
Since I think that it might be important to clarify in this thread: my view on abortion is that I am generally pro-choice, I'm... incredibly uncomfortable with the idea of abortion being legal right up until birth so some limitation might be required, but I'm not educated enough to say exactly when. I feel that the current laws in the UK are alright enough even though I'd like to see the doctors requirement removed but considering that has a very limited impact and that the vast majority of terminations happen very early in the pregnancy, its not something that I'd die on a hill over.
Interesting. Personally, I've talked to nurses involved in pre-natal and post-natal care, and my mom was a Labor and Delivery nurse. Generally, they're pro choice until 16-24 weeks. That said, it sounds like Europe is to the right of America on abortion, which is interesting since according to Atlas most Democrats would be rightists in Europe.