Asserting that an economy is in a liquidity trap is equivalent to asserting that increasing the money supply will not drive up inflation or interest rates in the short term, but will drive employment and GDP growth.

I don't think it makes sense to argue that this situation is not theoretically possible since it appears to describe reality quite well. That said, the policy commitment that comes out of accepting even the possibility that we may be in a liquidity trap should be uncontroversial regardless of whether you believe the model is a close approximation of reality or not: push aggregate demand until there is some evidence it is driving up inflation and interest rates, at which point the theory says to stop because more of the same won't do any better.