What is the difference between this hypothetical family budget and the US Government's budget?
One answer is: eight zeros, because these are essentially the US budget numbers with eight zeros knocked off.
A second answer is: Prisons and the printing press. Because the biggest difference is that in the family budget context, everyone sees these numbers as simply insane, while on the national level at least half of folks think they are just fine. The difference is that the US government can take money from other people at whim and by force, backed by the threat of incarceration. And if that fails, it can print money (actually using bits and bytes rather than the printing press, but that's just a detail) to pass the cost of its extravagance onto other people in the form of inflation.
Update: The chart above probably over-estimates the belt-tightening. If you really wanted a comparable situation to today's federal government, the example would say that the family spent $37,000 last year, proposed to spend 38, 285 next year, but agreed to only spend 37,900 for a $385 "cut", said cut being claimed despite the fact that actual spending will be $900 more than last year.