Here is one sentence to ponder:
The significance attributed to money in influencing output has fluctuated greatly as various aspects of VAR modeling have advanced.
It is instructive to read the first few paragraphs of that paper (and here), to get a sense of how murky the issues are. And that is looking at non-liquidity trap periods. If you want a more recent defense of the relevance of money, try this paper. Here is a more skeptical view. Either way, I defy you to come away convinced.
The evidence is much stronger that deflationary shocks are bad; see this Christina Romer and David Romer paper.
We do have theoretical grounds for believing that monetary expansions will be potent when there are lots of unemployed resources and when the demand for money has recently spiked up. But if we're relying on theory, theory doesn't tell us much about expected employment effects because we're back to Arnold Kling's point:
Pretty much everything in AS/AD is riding on the hypothesis that labor supply is highly elastic at the nominal wage and labor demand is reasonably elastic at the real wage.
This is another way of understanding why the Fed is afraid to inflate some more. The gain is uncertain, but the bureaucratic cost of coming out for higher inflation is pretty much for sure.
Mark Thoma's views on the asymmetry of monetary policy, across periods of falling and rising income, can be found here.
Overall, it is easier to break things than to put them back together again.