You can’t cut the cord in health care. Medicare and Medicaide are federal programs.
I'm very unfamiliar with these issues, so please don't mistake this for a rhetorical question. There are physicians who don't accept Medicare/Medicaid, aren't there? Then why can't hospitals refuse?
Medicare and Medicaid do not constitute *federal funding* -- they are the means some use for paying a hospital bill, those dollars happen to be federal dollars. Funding is an entirely different ballgame ... if the choice is between some federal dough to help pay for updates in the operating rooms, a new MRI, comfier chairs in the waiting rooms, etc., or being denied this money because the hospital policy is that children, regardless their age, are not killed in it, well, then that hospital simply needs to petition its other supporters, particularly those of the Catholic faith, to make up for federal dollars lost.
If what this order means is that anyone who comes to a Catholic hospital that refuses to perform abortions has Medicare or Medicaid deny paying the bill due for services he received in that hospital, well, to me, that smacks of a kind of religious intolerance, violation of the First Amendment, I would take this to all the way up to the Supreme Court if I were the patient being denied my legitimate bill getting paid.