A relatively minor, but important point:
The deficit is the annual gap between money received by the government and money spent by the government. For instance, say the federal government brings in $1.5 trillion in tax revenue in 2010, but spends $1.8 trillion. The deficit, or gap between income and expenditure, is $.3 trillion (or $300 billion).
The national debt is the accumulation of each year's budget deficit, so to find it you add up each year's deficit (and subtract any time there's a surplus), so the current national debt = budget deficit for year 1 + deficit for year 2 + deficit for year 3 - surplus for year 4 + deficit for year 5, etc.
Thus, the NY Times should know better than to say:
"The payoff in budget savings would be small relative to the deficit: The estimated $250 billion in savings over 10 years would be less than 3 percent of the roughly $9 trillion in additional deficits the government is expected to accumulate over that time."
This should be $9 trillion added to the national debt. Again, this is a minor point, but it's really important to note, when you're trying to, say, describe how much debt Obama is adding to the country (on top of mountains of debt added by Reagan and Bush) vs. the current gap (largely caused by the fall in tax revenues) in government income vs. expenditures.
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