The General Social Survey (a big long running social attitudes monitor since the mid 70's using the same questions which I like for consistency) shows support for the proposition 'Abortion if a woman wants for any reason' which is the phrase that covers the most 'open' rights to an abortion that even people who are pro-choice might feel uncomfortable has been rising from 30% in the early 80's to 50% in 2018 and rocketed in millennials from 29% in 2005 to 54% today (they used to the group least likely to answer in favour back then)
Conversely the 'not even if the result of rape' response is at 21% and the 'not even if the mothers health is seriously endangered' (!) is at 10%. That's been remarkably stable since the early 80's.
So you have a core 50% in favour of effectively no limits at all (with some nuance I'm sure) and 20% in favour of limits except for the most commonly held extreme pro-life position.
The last forty years has basically been the pro-life movement shifting US public opinion to more open and permissive support of abortion than European counterparts. On that basis, they should perhaps be wary of what some states will legislate for if it's left up to them by the Supreme Court.
Does the General Social Survey question ask about legality or moral approbation?
It's strength and weakness is that the main questions are frozen. So there's a question on abortion if a woman is 'not married and does not wish to marry.' As a set of questions abortion falls under policy, rather than morality which again may be of it's time, though some new questions have been added.
It did ask for moral opposition to abortion in it's most recent findings. 29% said they did (immoral), 28% said they did not. The rest answered 'it depends'. Only 30% said it should be harder to obtain an abortion.
Poll
