Going back to the OP, is a compromise possible? Certainly not one that will appease everyone, or, IMO, most people. On the pro-life side, you have a large group of people who believe that life begins at conception, and this abortion at any time is murder. They’re not going to say, “Well, okay, I guess you can murder an innocent child, as long as it’s before X weeks.” On the pro-choice side, you have a large group of people who believe that unless a woman can waltz into a hospital at 8 months, 3 weeks, and get an abortion, then her rights are being infringed by an oppressive patriarchal regime. These people aren’t going to be made happy by any sort of compromise.
Then you have the pro-life-lite side, who maybe would be okay with abortion up to about 2-3 months, albeit squeamishly, but anything after that is wrong (for the record, I’m kind of in here). These people will be okay with first-trimester-only abortions, likely. On the pro-choice-lite side, you’ve got those who are okay banning partial-birth and late-term abortions, but think the woman should be able to do whatever she pleases for the first 6 months. I would say that the majority of Americans who have any opinion on the matter fall into one of these two categories.
So where does that leave us? If we cut off abortions at the first trimester, we’re going to anger roughly 50% of the population. If we cut off abortions at the second trimester, we’re going to anger the other half. Cut them off somewhere in the middle, and you’ll just piss off everyone - pro-lifers will think it’s too late, pro-choicer will think it’s too soon.
We currently stand pretty much on the extreme pro-choice side, right now. A woman can pretty much get abortion-on-demand as late as she wishes, and the pro-life side is predictably irate. However, it appears that public sentiment is gradually shifting to to the pro-life side, such that we’ll probably see some kind of restrictions on abortion within the next decade or so. I think they’ll probably be minor, though - outlawing live-birth and partial-birth abortions, maybe something outlawing all abortions past 2nd trimester, and perhaps stricter laws on parental consent (which, in many areas is fairly lax, from what I’ve heard).
In general, I think the pro-choice side will maintain control of the issue in the forseeable future, but long term, who knows?