...how long it takes for the Eunach class to remonstrate one of their own who has dared to say monetary policy is not the panacea it is claimed to be.
Brad Delong, dismal scientist, is starting to come around.
In such a setup, the conclusion of Mankiw and Weinzerl that monetary policy has the exclusive role to play is straightforward: One stabilization policy tool--monetary policy--is non-distortionary. The other stabilization policy tool--fiscal policy--is distortionary. If monetary policy can do the job, there is then no need for fiscal policy. And if you do resort to fiscal policy, use the fiscal policy that is most effective at getting people to spend money on the things they were at the tipping point of buying anyway--use the investment tax credit rather than direct government purchases or tax cuts which might well not be spent. End of argument.
But are the assumptions correct? Can monetary policy do the job?
There is little  doubt that it can do the job--and that the conclusion is sound--in normal times, when the short-term safe nominal interest rate is away from its zero nominal lower bound, and when small bond sales to shrink and bond purchases to grow commercial-bank reserve deposits shake the entire intertemporal price structure. 
But does the same hold true in a liquidity trap, when short-term safe interest rates are at their zero nominal lower bound? At the zero nominal lower bound monetary policy as stabilization policy has two potential modes of effectiveness:
Even with short-term safe nominal bonds at par, the market flooded with excess reserves, and thus with reserve deposits perfect substitutes for short-term Treasuries, the monetary authority can take duration and default risk onto its balance sheet and thus free-up risk-bearing capacity to improve borrower access to credit.
Even with short-term safe nominal bonds at par, the market flooded with excess reserves, and thus with reserve deposits perfect substitutes for short-term Treasuries right now, the monetary authority can promise it will keep interest rates lower and inflation rates higher in the future than its standard reaction function would warrant.