If monetary policy is not distortionary--if it simply has an influence on the level of aggregate demand but no other real consequences--but fiscal policy is distortionary because it has the government buying things that are worth their cost only because of the aggregate demand externality, then of course fiscal policy should be set on classical principles and monetary policy used to stabilize the macroeconomy. That is what we should be doing in normal times.
But right now times are not normal. The dynamic consistency and credibility problems involved in getting monetary policy right in a liquidity trap are substantial.
Credibility and Monetary Policy in a Liquidity Trap (Wonkish): Via Mark Thoma, Mankiw and Weinzierl... argue... that fiscal expansion shouldn’t be the tool of choice even at the zero lower bound... if you can credibly make commitments about future monetary policy.... [This] isn’t a new insight; it was at the heart of my original analysis, and it’s a central theme in Eggertsson and Woodford. But how credible is the idea of credible future monetary commitments, of the type needed to make this work? Bear in mind that the central bank needs to “credibly promise to be irresponsible”, as I originally put it — that is, to commit to creating or allowing higher inflation....
[I]n order to make a commitment to inflation work, central bankers not only have to stand up to the pressure of inflation hawks — which is much harder when you’re having to testify to Congress than it is if you’re a Harvard professor — but, even harder, they need to convince investors that they’ll stand up to that pressure, not just for a year or two, but for an extended period.
Now, the thing about fiscal expansion is that people don’t have to believe in it: if the government goes out and builds a lot of bridges, that puts people to work whether they trust the government’s commitment to continue the process or not. In fact, to the extent that there’s some Ricardian effect out there, fiscal policy works better, not worse, if people don’t believe it will continue.
On a personal note: I supported fiscal expansion in 2008-2009 precisely because I didn’t believe that the kind of commitment-based unorthodox monetary policy that works in the models could, in fact, be implemented in practice. Nothing I’ve seen since has changed my views on that subject.