For the big concern about quantitative easing isn’t that it will do too much; it is that it will accomplish too little... The only way the Fed might accomplish more is by changing expectations — specifically, by leading people to believe that we will have somewhat above-normal inflation over the next few years, which would reduce the incentive to sit on cash.
Yes, somewhere there are households and firms that are sitting on excess money balances. And understand these are not the debt-strapped households and firms that should be refraining from further spending. No, these are the households and firms that are creditors and thus the beneficiary of the debtors who are now saving more. Instead of spending their growing stock of money they are sitting on it because they see an uncertain economic future. Here is the rub: it doesn't have to be this way. If these creditor household and firms all simultaneously started spending their excess money balances this would increase aggregate spending and in turn spur the real economy.* Moreover, knowing that the real economy would improve going forward would feed back and reinforce current aggregate spending. A virtuous cycle would take hold and push the economy back toward full employment. But this not happening, there is still an excess money demand problem. No creditor household or firm wants to be the first mover and spend his/her money for a good reason: there is no guarantee anyone will follow. This amounts to a negative aggregate demand (AD) externality.
In order to fix this AD externality one needs an entity powerful enough to incentivize all the creditor households and firms to start spending their money simultaneously. Enter the Federal Reserve. It alone can change inflation expectations and thus motivate these creditors to start spending. Note that by changing inflation expectations the Fed is really changing expectations of future aggregate spending, the source of expected inflation. And by changing expectations of future aggregate spending it is changing the economic outlook for the better too. The Fed, then, is the one entity that can kick-start this virtuous aggregate spending cycle. However, in the absence of an explicit nominal target to shape inflation expectations it is not clear to me the Fed will be successful in fixing this aggregate demand externality.
*It is not always the case that an increase in total current dollar spending will shore up the real economy. But it is the case now because (1) there is resource slack and (2) there are sticky wages and prices.