With respect to late term abortions, the percentage of "late" abortions is small, but over 90% are not fetal abnormalities or threats to a mother's life.
The most common reasons for late abortions are things like the sudden realization that a woman is not ready to be a mother, the "father" not stepping up, the woman having delayed for a host of reasons getting an abortion earlier. There is a study by the Guttmacher Institute on this, you might find interesting.
"The Guttmacher Institute also surveyed a large number of women obtaining late abortions and asked them their reasons for doing so. It found:
Only about one percent of second- and third-trimester abortions are performed for fetal anomalies, or eugenics"
Most abortions related to fetal abnormalities happen far sooner in the pregnancy. Modern ultrasound techniques are amazing at identifying issues like this and so women abort these babies far earlier.
I am not against abortions, I see a balance between their appropriate use and a baby's right to life. Circumstances not absolutes determine when an abortion is appropriate when it is not.
But back to your question, in those extremely rare cases where a late term abortion is necessary to protect the life of the mother, than certainly those abortions should be legal, I expect the courts will insure that is the case, if the laws passed by the states don't. But the issue revolves around the over 90% of instances where that is not the case.
Whether you change your position or not regarding abortion, I hope the information I provided is helpful. I am disturbed that the abortion debate is largely taking place over religious and political beliefs, when it should be about biology and human rights... both the woman's and the baby's.