One word: inflation!
When you adjust the dollars for inflation, the discrepancy might not be as large. That sort of math is beyond me, but I am certain that inflation plays a role in the figures that are being used.
Compare the rates of federal government spending on programs like Medicaid, WIC, food stamps, housing subsidies, college grant money, CHIP, NAFTA-TAA, SSDI and so on with the rate of spending on these programs in the 50's or 60's.
In this area the average federal government housing subsidy is $400 a month and housing is relative cheap in this area. In some areas the housing subsidies average $700 a month and more.
Then look at government spending on Medicaid. And the wasteful NAFTA-TAA programs which accomplish almost nothing.