This paper, from George Evans via Mark Thoma (original here), shows why fiscal stimulus must be greater than a threshold level to be able to kick an economy out of stagnation. Obama’s stimulus was clearly too small.
Mark Thoma:
“Escaping from the stagnation trap requires a change in government spending or some other shock of sufficient size. If the change in government spending is large enough, the economy will return to full employment. But if the shock to government spending is below the required threshold (as the stimulus package may very well have been), the economy will remain trapped in the stagnation regime.”