In the longer run, the legislation would result in a slight decrease in gross domestic product(GDP) compared with CBO’s baseline economic forecast.
More importantly, the CBO underscores that stimulus cannot provide long-run growth if it only increases demand without increasing our productive capacity. According to the letter,
Even if the fiscal stimulus persisted, however, the short-run effects on output that operate by increasing demand for goods and services would eventually fade away. In the long run, the economy produces close to its potential output on average, and that potential level is determined by the stock of productive capital, the supply of labor, and productivity. Short-run stimulative policies can affect long-run output by influencing those three factors, although such effects would generally be smaller than the short-run impact of those policies on demand.
This statement provides the integrated short-run (Keynesian), long-run (classical) framework that causes aggregate supply to have very different properties over time. Without increases in agrregate supply, the stimulus could lead to inflation if an increase in demand must adopt to lower long-run supply. It may of course be that we are operating below the long run supply (the exact arguement that stimulus supporters will use high unemployment numbers to make). If so then the timing of the stimulus again becomes important.
Even strong Keynesian's like Steve Fazzari have noted that what we spend our money on matters. Increases in education or training may increase long-run aggregate supply spending on infrastructure may not if we are just using old techniques to repair roads, etc.
It should also be noted that the CBO report provides a wide range of possible impacts from the stimulus. For instance it indicates that the plan could provide anywhere from 1.4 percent over baseline increase in GDP to 4.1 percent in 2009. Sadly, the estimates are non-stochastic (or at least not presented as such) so their likelyhood is more difficult to determine.