No one is happy with the American Healthcare System unless you have America's exclusive socialized Healthcare, Tricare. You're also calculating it off of part time hours.
However, depending on how you define "socialized", lots of people are covered under several "socialized" programs by the US government, not just Tricare. Medicare (old or disabled people), Medicaid (the very poor), CHIP and things like that (poor kids). Also, if you're counting Tricare, probably any health insurance provided by any level of US government (federal, state, county, city) to government workers should count.
In the end, the US government pays for healthcare (or, at least, much of it—US prices for healthcare are very high, and the way our insurance works means that insurance is just part of how the bills get paid, though a large part) for an high percentage of our population, one way or another.