It would seem to me once a woman gives notice of her intent to abort a child, that child has had any and all legal rights revoked. That would by necessity include citizenship.
I think that child now has a claim of seeking "political asylum" as an illegal alien, they're just at a different boarder.
An astute attorney could tie this up in the courts for a decade or so. Meanwhile abortions would be stayed until such time a opinion is issued.
Won't work.
