It is damn hard to predict the future, there are chronic illnesses people can suffer from for decades where they pretty normal lives as long as they get medication and some checks and such. With some of those illnesses just the cost of medicine can be $100 a day or even more.
Now I have not tried to do any of the complex math needed to see what it would mean for taxes in the US if universal healthcare becomes a thing, but two things are certain.
A. Thinking 18% of ones paycheck will cover health care and college tuition "very easily" doesn't guarantee anything. For most it will, but not for everyone.
B. Currently the US spends like double that of most nations on its healthcare - and that is with aprox. 10% without coverage, many more with insufficient coverage and many others with coverage where co-payments are insane. In other words there is enough money in the US health system to cover all right now, the trouble is the multi payer system makes for a inefficient and costly so a lot of the money right now goes to insurance companies and overpaying the medical sector.