A phrase often used by Keynesians, Old and New, in these times is "pushing on a string". Whatever the origin of the phrase, there is a reasonable amount of common sense to it. By saying the phrase, Keynesian economists mean that creating more monetary base, i.e. more money, does not really create more demand for it when interest rates are as low as they can go (0 percent). The main monetary channel at this point is through inflation expectations. But how can a central bank demonstrate its commitment to raising inflation and keeping it elevated in future years when it's credibility, which it has built up over the years is on the other side of that coin?
Despite being an ad hoc (not microfounded) macroeconomic model and that obviously the idea that prices are essentially fixed, the IS/LM model of the liquidity trap pretty easily shows that the adoption of loose monetary policy does not necessarily imply an increase in output (gross domestic product). It could be that it would be effective at raising output, but that would be triggered by one of two things (that come readily to mind), decreasing the real interest rate, which would make it more cost effective to invest, or by devaluing the nation's currency, which should decrease a trade deficit or increase a trade surplus. Both of these hinge upon expectations. After all, it is only the expectation of increased inflation that can decrease the real interest rate when the nominal interest rate is unable to be cut. Similarly, affecting exchange rates has much to do with expectations, since higher expected inflation would portend a depreciation in a currency, according to the purchasing power parity theory of exchange rates (which works fairly well in the long-run).
As Paul Krugman often points out, changing inflation expectations when a liquidity trap prevails generally implies a credible commitment by monetary authorities to allow higher inflation after liquidity trap conditions have passed. In other words, there has to be a commitment to be "irresponsible". Several Keynesian economists seem to believe that is a policy that is easier to announce than to implement. It seems like it might be best to pair this with something that is very likely to work, an accommodative policy by the Federal Reserve Banks supporting a substantial federal fiscal stimulus, spent on infrastructure and education.