In fact, hospitals are arranging to deport people. Yet another place where undocumented immigrants will have an incentive not to trust the authorities in our society. They're already so paranoid about the police that they won't help us investigate crimes; now it's doctors; soon they'll be resisting interactions with the grocery store clerk. If we end up with an epidemic of something, because most members of an immigrant community were afraid of getting treatment, I'm going to blame people like Lou Dobbs.
We would, in fact, be much better off just having universal care, even if some of it "leaks" into care for the undocumented. In the absence of universal coverage, non-emergency care is unavailable to millions of people, citizens and immigrants alike. Those people can't afford an ounce of prevention, so they show up at the ER in need of a pound of cure. Unless we're willing to have people literally die in the streets outside those ERs, we have to treat them. Then we ruin those people's lives (collections agencies, taking their cars, their houses, or, in some cases, deportation), and still don't manage to pay the bills they run up. So then the excess cost gets passed along into the bills of insured people, raising the cost of care, and eventually causing more people to become uninsured.
We'd end up paying less if we just provided the preventive care in the first place.