Everything Yglesias writes here is quite right. For now, I'll refer people to my rough and ready guide to the problems with Medicaid (i.e. the public health care for low-income people), written a week or two ago. It's useful, I hope. And if you walk away with the rather perverse conclusion that the program ought to be expanded in many ways, not slashed, then you've read correctly.

It's also, I should say, a bit ingenuous to say that Medicaid is running at lower costs than the private insurance system, since it's certainly true that Medicaid leeches off the private system—mainly by contracting for its services at lower-than-market prices, thus forcing doctors and hospitals to cost shift onto private payers. But the president's preferred policy doesn't fix any of that.