Until we have a cure for the metabolic syndrome, I'd say that comparison of health care quality by life expectancy doesn't actually do what you think it does. America is incredibly obese, and this is a lifestyle choice that makes comparisons of the quality of care quite difficult.
I wouldn't even try to make the argument that public healthcare doesn't work. Comparing across systems and cultures (again, obese vs the rest of the world) is tough to do well. I was thinking perhaps some measure of in-hospital mortality would be useful, but even that would be confounded. Perhaps the Massachusetts model might work for in-US comparison to other states, but MA is not really comparable to single payer systems in the rest of the world.
It's a really interesting topic and I wish I weren't at work so I could brainstorm more with you about how to get a clean comparison.