I sometimes tell people my main objection to Obamacare is that it's not Single Payer. That's glib and not altogether true. But I don't expect the U.S. to embrace Single Payer in my lifetime and pressing for it is largely just a way to get whatever health care system we do have to be more comprehensive and responsive to the uninsured. It's like how some folks are now demanding the minimum wage be doubled, hoping that if that movement seems loud enough, it might result in a compromise to raise it by, say, a third.
But why not Single Payer? Well, it has its problems, above and beyond the fact that this country will never go for it. Ezra Klein discusses some of them.