unless you are part of the 47% who pay no taxes and rely exclusively on government
This is factually wrong. While 47% of households paid no federal income tax for 2009, only 14% paid neither income nor payroll tax. Also, people pay sales taxes at the state and local levels.
If you pay no federal federal income taxes then you are receiving benefits from the federal government (national defense, food security, protections from federal regulations) but are paying nothing in return.
If it actually worked that way, you would be correct, but it doesn't. In actuality, any surplus money, of which you can consider the lower income brackets to be contributing a certain proportion of, has gone into treasury bonds, meaning intra-governmental debt has been created so that other areas of the government can spend it. The government always finds a way to do whatever it wants with the money it gets from people.
if someone was paying their fair share in taxes then the government would need to borrow a little bit less then what it otherwise would need to. If the entire 47% of the people who pay no federal income taxes paid their fair share of taxes then the government would need to borrow a lot less (or potentially be running a budget surplus)