Is Fiscal Stimulus Just Stupid?

Greg Mankiw uses rhetorical questions to argue that the government should not be using fiscal stimulus to prevent a recession. He asks (in my words):

If monetary policy is the strongest lever, and if fiscal stimulus limits the Fed’s monetary options–ties their hands–why are we considering fiscal stimulus?

But he’s posing it as a zero-sum game, hence an either/or decision. (Fairly typical in academe: flaming controversies asking "is X true or is Y true," when the obvious answer is "yes.")

Consider identical questions an investor might ask:

It’s clear that over the long term, small-cap value stocks outperform other asset classes.

If I put money into other asset classes, that reduces the power that small-cap value stocks have to increase my returns.

So why should I invest in any other asset classes?

This question-series-cum-argument sounds silly, because every one knows that it’s not a zero-sum choice; diversification improves the return-to-risk ratio. (It’s "the only free lunch.")

So, rather than trying to answer the $145-billion-dollar question that Mr. Mankiw is so much better qualified to answer, I will ask it of him:

Is what’s true for portfolio returns also true for efforts to stimulate the economy?

Do fiscal and monetary stimuli combine to deliver more than the sum of their parts? 

In other words, can fiscal stimulus help reduce the "risk" of unemployment, outweighing the constraining effect of increased inflationary pressure?