Taxes and Charity?

It just occurred to me to wonder, and I figure someone must have done the math already, but if not, someone should. What percentage of the money we give to the government in taxes goes to charity, in the sense of humanitarian aid? How much of what I pay goes to feed the hungry, to clothe the naked, to heal the sick?

In the past, I've assumed that number exceeded 10% of my income. I'm suddenly curious if it really does. Does the government, with all the money it forces me to give to all sorts of places, in all sorts of ways, have the effect of forcing me to meet my minimum duty of tzedakah? Can I relax in knowing that anything I choose to give is above and beyond? If not, how much more need I give before I cross that line to where it's what I can and choose to give rather than what I must or am expected to?