Depends on what you mean, by "South of the Border".
Texas is already getting a net gain of Doctors and some pretty hefty improvements of medical services, mostly ever since the state of Texas passed tort reform for medical services.
(Ie, you only get a limited amount of money for mental distress, but you aren't exactly limited, on medical services, if the practitioner messes up. And the biggie, lawyers can only get so much money.)
Heck, the dinky local hospital has a da Vinci Surgical System. (Can be used for heart surgeries, or even reversals of vasectomies.) This was of course, ever since the local government handed over management to a private company. (Catholic run). We are going to try and get a Medical school, in the city, going soon.
Not to mention already having Medical Zones, in some cities. (Big tax breaks, for businesses and practices, if set-up, in certain areas)