2009: -1.2%and 2.9% thereafter (table S-8). In his elliptical fashion, Greg Mankiw hints these projections might be criticized as unduly optimistic. The "blue chip" average of private sector forecasts are indeed somewhat lower (in a display of Obama-era "refreshing honesty" these are included in the same table of the budget). For reference, over the period 1948-2008, the average annual growth of real GDP is 3.36% (2.88%, 1974-2008).
While Yogi Berra was right that "its tough to make predictions, especially about the future," there is good reason to expect above-average growth coming out of the recession. The Solow model gets things basically right about long-run growth in the US: our economic capacity increases fairly steadily over time due to technological progress and population growth. During a recession, resources go under-utilized (e.g., unemployment occurs) and the actual amount of output falls below capacity (a.k.a. "potential output"). But capacity continues to grow, creating a growing "output gap" between what we are producing and what we can produce. This picture from the CBO's January forecast is a good illustration: Notice that the recovery - closing the output gap and catching back up to the long-term trend - necessarily involves faster than average growth.
Some object to comparisons with the 1981-82 recession (the causes were very different), but it was the last downturn of similar magnitude to the current one. While 1982 was a very, very bad year - unemployment peaked at 10.8% in November and December - the recovery saw several years of rapid growth:
1982: -1.9%At Econbrowser, Menzie Chinn has more discussion, with illustrations, of the issue. On his new blog, OMB Director Peter Orszag explains the gap between the administration and CBO forecasts.
1984: 7.2% (!!!)
Update (3/3): The CEA makes the same point, with evidence. Mankiw is skeptical.
Update #2 (3/3): Brad DeLong weighs in, responding to Mankiw.