I don't know if it's a huge problem for public policy, but it certainly seems like some kind of problem that, as Matt Yglesias says, most everyone has trouble processing differences between large numbers. That handicap is why the Obama administration can propose $100 million in cuts from a budget of trillions and expect something other than to be laughed out of Washington. It would be kind of funny if Dr. Evil hadn't already made this joke a while ago.
That said, I thought Matt's solution to this problem was not altogether satisfying:
Oftentimes when talking about budgetary matters in the United States, I think it would be helpful to come up with something other than raw dollar totals to discuss. Talking about a given initiative costing $X per person or per household, or being such-and-such a percent of total economic output, might give people a better understanding of the relative costs of different things.
Would it? If you take the size of the budget and divide by the number of households in the country, you will end up with the mean but not the median cost per household. The problem is that this would give people a better understanding of the cost only if we lived under a government that levied some wacky head tax -- a lump sum tax on every person, regardless of income -- rather than a country with a progressive income tax.
Maybe some futuristic high-tech version of the New York Times could automatically scale budget figures to your tax burden -- I'd subscribe to that -- but until then I fear we'll have to live with our imperfect brains and their imperfect command of the budget.