The economic theory behind QE has always been flimsy. The original argument, essentially, was that the absolute level of prices in an economy is determined only by a central bank's supply of base money. Because of this, at least in the long run, any increase in supply must raise prices proportionally. It followed that, in the short run, QE must also have an effect on spending levels, that will eventually tend to raise prices, even if the channels by which this occurs are obscure.
The problem is that, for this theory to apply, there must be a permanent increase in the monetary base. Yet after the Bank of Japan's experiment with QE, the added reserves were all rapidly withdrawn in early 2006. More worryingly for Mr Bernanke, whatever the long-run effects would have been, there was no increase in nominal growth over the five years of the experiment.
The Fed has given no indication that the current huge increases in US bank reserves will be permanent. It has also promised not to allow inflation to rise above its normal target level. So for QE to be effective the Fed would have to promise both to make these reserves permanent and also to allow the temporary increase in inflation that would be required to permanently raise the price level in that proportion.