In order to take a look at how the US economy has fared in past periods of deficit reduction, below is some important data linking GDP growth to deficit contraction. The chart shows the data for every year that there has been a contraction in the deficit as a percentage of GDP since 1929.
Over that time frame there have been 42 years that the government has spent less money relative to GDP than it did in the previous year, and the good news is that in the vast majority of those years, there has still been positive GDP growth. Real GDP only contracted in 7 of those years and Nominal GDP only contracted in 3 (two of which were in the depression). The reason that nominal GDP has fared better is that there is actually a strong history of inflation in years of deficit reduction--something to definitely watch for in 2013.
|Source: Federal Reserve|
If the deficit shrinks by the full fiscal cliff amount of ~$500B next year, that would mean that the deficit would shrink by ~3% of GDP. Below is some data to put that into context relative to other years in which the deficit contracted by a large amount in a single year. Many of the data points are clustered around the post WWII period (when we ran our largest deficits captured by the data), but low real GDP growth and high inflation are characteristic of most of these years.