Be careful what you wish for.
In European countries most citizens pay upwards to 50-60% of their "taxes" to the government. There is very little of this tax shifting, mortgage interest deduction, 401K deduction that we have in the United States.
Plus Universal Health Care means a "limit" on what the government considers non-essential health services. Yes, that does mean, they are not going to rescue that pre-term baby born at 25 weeks while in the United States, we do all that is necessary to save a life.
They basically play god with your health needs. The government determines what and what doesn't need to be done.
Do you think Bill Clinton would have gotten his Heart Bypass surgery within 24 hours (Regular US citizens also get heart surgery within 24 hours if indicated so I'm not using Bill Clinton as an example).
No, in Universal Health Care societies, unless it is an absolute emergency, Bill Clinton (or those with the same heart conditions) would have had to wait upwards to 6 weeks for the surgery.
But then if you are without health insurance, like millions of Americans. You have to pick which finger to fix (by accident) as depending on what finger, the bill goes up. I have seen a child dying because the hospital that the insurance sponsor is far from home and the insurance will not pay for penicillin to the hospital near the baby home, because it is not a hospital sponsored by the insurance!!
See, even thorough i don't see the NHS in UK as a sustainable system, i still prefer it to the American system from the humanitarian point of view.