I do not think targeting nominal GDP means that the monetary authorities can achieve that target at all points in time. The main way I think it overcomes the zero lower bound (ZLB) for nominal interest rates is by promising to create higher inflation in the future, which is itself a cost. The more austerity reduces current demand, the more inflation we will have in the future to counteract it.
So the argument for using deficit spending rather than monetary policy to raise aggregate demand is that deficit spending will produce a significantly lower path of inflation in the future.
I am sure that somebody can come up with a model under which this is true. But how many macroeconomists would sign on to such a model? Back when I was doing macro, nobody would have done so. AD is AD, whether it comes from monetary policy or fiscal policy.
I'll admit that I am probably not the one to be carrying this particular fight. I think that all of macro is likely to be mistaken (see PSST).