I'm one of the posters that's OK with the current law and term limits (though I think 24 weeks is on the low side), but for practical rather than moral reasons: I don't think unborn babies are sacred and I do care about distressed women in late pregnancy - but they are rare, and could be helped without killing the fœtus.
I agree that abortion on demand up to full term is morally consistent, because a blastocyst and a full term fœtus are of equal worth, in that they carry equal potential. The difference is in the sacrifice required of the woman (in terms of morbidity/mortality risk, social consequences, and the experience of gestation and delivery) in order for that potential to be realised.
By 28 weeks (say), the woman has already suffered most of the medical and social consequences. Her body has changed, she is visibly pregnant, and she is unavoidably committed to going through delivery. For her to continue to be pregnant for another 9 to 12 weeks is not a big concession.
As full term approaches, the medical consequences, and the woman's subjective experience, converge for the two possible outcomes - of live birth and deliberately induced stillbirth - to the point where the only real difference between the two scenarios is in whether the child is alive or not.
Rationally, even if we accept that the woman's welfare is paramount, I would still like to know - how does it assist her welfare for a child to be dead rather than alive (all other things being equal)?