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 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.