here are my two simple ways of thinking about fiscal stimulus.
from the perspective of the stimulee: the federal government is right now the cheapest source of capital. in fact capital has never been cheaper. the treasury can borrow at record low interest rates. unfortunately the banking system is not doing its job as an intermediary channeling this credit to the bridge-builders. so the bridge-builders effectively borrow directly from the source by accepting stimulus dollars and promising to pay them back in the future with taxes.
(of course there is a wedge between the amount i receive in stimulus ($X) and the amount I pay in taxes ($X/N) and this makes me inefficiently eager to accept it. this is why stimulus should focus on public projects where the benefits are dispersed equally.)
from the perspective of government. we accept that there are things government should be producing, in particular public projects where the benefits are dispersed equally. the government has flexibility in the timing of these investments. since the investment requires coupling labor with the government’s capital, the optimal timing is during times of (otherwise) unemployment when labor is relatively cheap.
so we don’t have to think about multipliers and we don’t have to think about Keynesian effective demand. The government acting optimally to smooth expenditures should spend a lot now. Yes, it means spending must be correspondingly reduced in the future and critics would worry that this won’t happen. But there will come a time when interest rates are higher and it is more costly for the government to borrow and under pretty much any theory you have of how spending is determined, at the margin at least, that will have the effect of reducing spending.