Brad Delong writes
The principal argument for monetary policy is that, by modifying asset supplies and thus asset prices, it induces households and businesses to boost their spending on things that they almost bought anyway. Thus–for marginal policy shifts, starting out at a first-best optimum, and if the relative distribution of wealth corresponds to social welfare (or if questions of the relative distribution of wealth are left to a more openly political process and walled-off from technocratic macroeconomic questions of stabilization policy)–monetary policy will not push you far away from the free-market optimum.
Fiscal policy, by contrast, works through expanded government purchases ΔG. These must be financed by distortionary taxes to amortize the debt in the future. These taxes do drive a wedge between the social and the private values of output in the future. And what the government buys is determined by a political rather than by an optimizing economic logic. 
Before we get into the relative merits I want to stop and ask whether or not this makes sense.
How can these two instruments have this fundamental difference?
I understand how to walk through the steps in our standard model, but when we get to the end my intuition says, something has gone wrong here.
Two paths from point A to point B must wind-up having equivalent offsets. For each time the northern path zigs while the southern path zags the northern path must have some offset zag when the southern path zigs.
Otherwise one cannot end up at the same place.
Right now I am not certain how it works out by my intuition says that when fiscal policy fades, monetary policy must expand or else the price level in the future will be lower than what it otherwise would be.
This expansionary monetary policy causes nominal GDP to exceed the interest rate and amortizes the debt.
That may not be the right answer but I do feel like something is missing.
To be clear I am not saying that Brad or the standard reasoning is wrong. I am just saying that I am not intuitively squaring it.
It seems either that somehow the paths balance or the difference in the paths is equivalent to the difference in end points. So that you don’t actually get to the same B.
But, then that tends to suggest that sometime we amortorize debt through taxes and sometimes not.
You see I just don’t have it squared.