Would not medicare/caid payments be for services rendered?
Yes, but it's still federal money. They won't get paid for the services they DO provide if they refuse to provide Obama's OTHER services as well.
Years ago, when I worked in a bar in Minneapolis, the city passed a law that bars could only be open on Sunday if they served food. The owner of the bar bought a couple of TV dinners and put them in the freezer - in case we were ever inspected, those were the Sunday dinners. Possibly a hospital could stock abortion equipment from the sixteenth century and say that abortions ARE available, and here's the instruments we'll be doing them with.