What if stimulus works -- but only in theory?

Since the financial crisis hit, we have borrowed and spent $5.7 trillion, or 41% of 2008 GDP (7.8% of total GDP over the period). That is an enormous sum. Presumably, it has raised output somewhat higher than it otherwise would have been–just as an accounting identity, it would almost have to–and yet it has left us with unemployment in the range of 8%, and per-capita GDP that is still below the pre-crisis trend. How much would have been needed to force that growth back up to trend?

On Professor DeLong’s chart, the output gap seems to be about $4,000 per capita, or $1.25 trillion. In the context of our ongoing debt, that doesn’t actually seem to be so much. If you assume a multiplier on the high side, we would only need to have spent something like $600 billion dollars, perhaps over a series of years.

But this seems simultaneously too much and too little. Can it really be that adding $125 billion a year would have solved all of our economic woes? The US government has consistently gone over its projections by at least that amount several times over the last four years, and yet we are not better.