I think there is an obvious disconnect here in that the vast majority of folks against late term abortions are presuming the baby is viable.
I think most people agree on these anecdotal accounts about babies who couldn't survive outside the womb, but that counsels in favor of creating an exception, not a rule in favor of late term abortion.
It seems crazy to me this is a controversial stance, but I think the general thought on late term abortion from pro lifers is this: at the point a baby could be born (either naturally, induced labor, or c section) and survive without any significant medical intervention, then "abortion" is really just infanticide within the womb.