It seems to me that in the 20th century, when a recession was coming on the federal government provided money to state and local governments to cushion the shock of decreased tax income. This didn't happen post-9/11 and it doesn't seem to be on the table now. Certainly Providence's budget has been tight throughout; even during the bubble-fed boom, the schools have seen significant program cuts. As a new recession begins, we're already slipping far into the red at both the state and local levels, and I don't even know at what point dropping property valuations start to lower property tax revenues (the main source of school funding in the US for those of you living in more rational parts of the world).
Another answer is for the government to spend the money directly — or simply refrain from spending cuts that would otherwise happen. For example, state and local governments, which aren’t supposed to run deficits, may be forced to slash spending in a recession; aid to these governments can avert these spending cuts, which is a real plus for the economy.
All of this suggests that if you want a stimulus plan to actually affect demand, it should focus on people likely to be liquidity constrained and on sustaining government spending.
Since we're really talking about preventing cuts rather than starting new programs, there is no delay in coming up with ways to spend the money. It is the right way to do stimulus.