Third Way did a bunch of polling (PDF) in support of their new messaging report on the subject. In one section, the questioner says "I am going to list goals for some legislation before Congress regarding abortion. On a scale of 0 to 10, please tell me how strongly you support that goal, with a zero meaning you do not support it at all, a five meaning you are neutral toward it, and a higher number meaning you support it." Here's a couple of results:
People, in short, are pretty evenly divided on the question of banning abortion in all but the rarest cases, with 45 percent of the population having a pretty positive take on this abortion-banning concept. But the public is horrified by the idea of enforcing such a ban with prison time. That's not contradictory, as such, maybe tons of people think abortion should be illegal but punished merely with a light fine. It doesn't, however, make very much sense given the importance of the competing issues in play.