I don't think abortion is unpopular with Americans. A majority still want it legal. Granted, a majority would limit 3rd term abortions and more and more are opposing it, but abortion is not the peg I'd hang my hat on for saying America was on my side. Maybe leaning my way, but we're not there... yet.
I agree with everything else you've said. Keilo is enormously unpopular. Same thing with gay "marriage." Civil rights? I mostly just roll my eyes at these, as there's generally a shrill voice and thin skin on the other side of the squeals.
Abortion is one of the weird issues.
Poll after poll say Americans want it to be kept legal, poll after poll shows that Americans have never met a restriction on abortion they didn't like.
FWIW, the polls are kind of screwy, some polls allow folks who want abortion banned with exceptions for rape, incest and threat to a mothers life to be considered in the "want abortion legal" camp, while others list them as pro-life, its why the polls are always all over the place on the issue.
A strong majority do hate abortion on demand though, and that can cost dem votes.
You are right about a majority of Americans wanting to keep it legal, but that is not the same thing as them supporting it. It is indeed unpopular. When it comes passing laws in favor of it, I expect those laws to be very restrictive, even in liberal states.
This is less about whether abortion is legal than about my need and right to petition my government on the issue. The best the Supreme Court can do is throw out Roe V. Wade, in which case abortion stays legal till each state can pass legislation on it. There is no chance the Supreme Court is going to find abortion unconstitutional. I want the opportunity to work at the State level to either make it illegal or to restrict it. I may lose, but at least I won't have been robbed of that opportunity by a bunch of justices who legislated from the bench. I think it is highly unlikely abortion will be outlawed in any but a very few states.