I always thought the unit root thing involved a bit of deliberate obtuseness — it involved pretending that you didn’t know the difference between, say, low GDP growth due to a productivity slowdown like the one that happened from 1973 to 1995, on one side, and low GDP growth due to a severe recession. For one thing is very clear: variables that measure the use of resources, like unemployment or capacity utilization, do NOT have unit roots: when unemployment is high, it tends to fall. And together with Okun’s law, this says that yes, it is right to expect high growth in future if the economy is depressed now.
A different economist, Harvard's Greg Mankiw, took issue with this sentence from the Obama Administration:
a key fact is that recessions are followed by rebounds.
Mankiw then went on to add his own nonsense to the debate. Now Mankiw has challenged Krugman to a wager.
I can simplify all of this for both of the Ivy Leaguers. The Obama Administration needs the world to believe that there will be substantive growth in the future. If the economy continues contracting for many years, the ability of the US government to repay existing debt holders will be in jeopardy.
Future economic growth is anyone's guess. All we can say for certain is that the actions of Washington in the past month have made future growth less likely than it would have been had Washington not done anything.