There's no need to raise taxes, just provide universal healthcare. US is already spending as much per capita on public healthcare to European countries![1] This means that instead of tax hikes you would need to use the existing budget for public healthcare to provide free public healthcare to everyone, just like all other countries who provide a "free" public healthcare paid with taxes.
How did they arrive at $4000 per capita on health expenditures? Times 300 million people, that's $1.2 Trillion. DHHS including Medicare and Medicaid was $940 Billion in 2013.
Anyway, I'd love to see a system that reallocated the money that the government is spending right now only on certain groups and used it to provide the best boost to public health it could for all Americans. But you would be running right into the AARP lobby who would frame this as taking care away from seniors. That's a fierce lobby, and you'd need some sort of plan.
[1] http://www.marketwatch.com/story/10-countries-that-spend-the...