Fed chairman Ben Bernanke earned the nickname “Helicopter Ben” after he remarked in a speech that in a fiat money system deflation can always be avoided by dropping money from a helicopter.
Based on my understanding of the federal reserve system, I believe the fed actually does not have the authority to do a helicopter drop. Under its current authority from Congress, the Fed can only give out cash in exchange of high quality collateral. So the only kind of helicopter drop Bernanke can do is if the helicopter has a big vacuum which can suck up collateral from the ground while dropping cash.
Therefore I do think that if we hit a deflation trap, it is possible that the fed may ultimately be unable to do anything about it. The reason is that if we do get deflation then the public may be comfortable sitting on the cash since it will gain value every year. So even though the fed maybe exchanging cash for assets, that cash may not really circulate in the system. We are sort of observing a little bit of this phenomenon right now as the excess reserves in the banking system keep increasing.