We spend more on Healthcare and education per capital than almost any other country. Don't let people bullshit you on the amount spent. Now results on dollars spent is a different question with a different answer.
We spend more per capita just in public money than some peer states do to provide universal healthcare, while ours isn't universal.
It makes more sense when you consider how many programs we have—a pretty high percentage of our population is covered by public spending, and—crucially—the ones who are are in some cases among the most expensive to care for.
1) Medicare (old or disabled)
2) Medicaid (poor)
3) Tricare or whatever they call it now, since I think the name changed (active and IIRC retired-with-full-benefits military and their spouses and kids, at least for the active-duty ones, can't recall if that part carries over in retirement)
4) VA (military veterans, including those with short terms of service)
5) Federal employees
6) State employees
7) County employees
8) City employees
9) Cops and firefighters and such, if not covered under any of the above.
10) School district employees (there are lots of these)
Not all of these are cases in which all the spending is covered by public money, but some of them are, and in other cases a great deal of it is. Also I've probably missed some programs.
[EDIT] Oh and that's not counting public money that goes to private companies but ends up paying for healthcare for those companies' employees and families, who are employed expressly to work on those publicly-funded projects—I can see arguments either way for counting that, depends on what you're trying to understand.