I loved that Obamacare (supposedly) touted the principle of making sure that an unexpected medical cost (surgery, broken bone, etc.) shouldn't mean financial ruin for an American citizen. The problem is that as a whole, there was no way that we could pay for it.
I still strongly favor the idea of competitive, inter-state health insurance plans covered through private markets. Yes, it would HAVE to be regulated. But competition and choices are what could keep the costs competitive. A blended approach like you mention would probably work best (maybe single-payer to cover the basic stuff like preventive care, supplemental to cover big unexpected events).
And the next piece of this discussion, which my favorite liberals like jimbasil and Chris and I have debated about before, is that the border has to be secured. These services have finite funding and resources, and if we don't secure the border, there will be a flood of people coming in that we can't support.