That's the thing ... the "health" exception is, in practice, abortion on demand until the moment of delivery. That's why the Democrats insist on it.
Any woman who's well on in pregnancy has some "health" issues. I'm 22 weeks into my 10th pregnancy. My hands and feet swell up late in the day. I have painful muscle spasms if I don't take enough calcium pills. I have fainting spells from time to time. Any of those symptoms (more added each week until Baby Whatsis makes his appearance in the outside world) is an adequate "health of the mother" justification for abortion, assuming I wanted to look for a doctor who would do such an evil thing.
Additionally, in three or four weeks, my baby would have a good chance of surviving if my condition necessitated an early delivery. Almost all really serious conditions in pregnancy (some exceptions for emergencies) can be handled for a few weeks with medication, bedrest, etc., until the baby has a chance to survive premature birth.
All the best to the new addition to your family, by the way.