Much of the debate over fiscal policy has occurred in Keynesian terms but its worth pointing out that it's perfectly reasonable to discuss fiscal policy in a monetarist framework. Start with the quantity theory of money MV=PY, money times velocity equals prices times real output.
In the long run we know that real GDP is pinned down by real factors (labor, capital, technology, institutions and so forth) so increases in M will increase P proportionally. But in the short run there are plenty of reasons to think that increases in M can increase Y – this is accepted by monetarists, Austrians, rational expectation theorists (ala Lucas) for unexpected changes in money, Keynesians and new Keynesians (only originalist RBC type theorists would object.) But M and V enter the equation in an identical fashion and thus logically must have the same effects for the same change. Thus if you think money is potent then V must be potent as well and V is fiscal policy.
To be precise, V is how fast money turns over and we can think about shocks to V as spending shocks. Spending shocks can be driven by consumers or by the government – this is what Brad DeLong means when he says "the government, in this respect, is just like any other group of starry-eyed optimists whose eagerness to spend pulls the economy into a high-employment, high-pressure boom."
One way of understanding the current recession is that V has fallen by a lot and it is dragging down Y (just as would a sharp fall in M). We can counter with an increase in M (monetary policy) or by an increase in V (fiscal policy).
Now we might think that V driven by government is too slow or too wasteful (ala Kevin Murphy (pdf)) to work well or we might think that neither increases in V nor increases in M would be as effective as Keynesians imagine since there is also reverse causality (falls in Y and expectations of slower growth in Y are reducing M and V). We could pursue the last point to its fullest and abandon the quantity theory altogether (making V an endogenous function of Y, for example, and removing it as an independent variable). But if we hew to the basic ideas of the quantity theory–and remember, it's not a true model only a way of looking at the world!–then fiscal policy is not impossible.