Quite surprisingly, although there is so much talk about the liquidity trap and its close concept, the zero lower bound (see the definition of liquidity trap), the criticism of these concepts is rather thin. This is even more puzzling since the liquidity trap concept is known for a long time, ever since Keynes proposed it (Rhodes did not find any mention of it in the work By Keynes).
To properly discuss the liquidity trap criticism, I would start by mentioning the two different understandings of this concept. In its original view, the driver of the liquidity trap is the “liquidity preference”. In a typical IS-LM model, once the interest rate hits a sufficiently low interest rate, the demand for money practically becomes infinite. In the modern interpretation, the liquidity trap emerges in a zero lower bound situation and it depends not on the current interest rate (as in the IS-LM model) but on future expected interest rate (as in a typical DSGE model). Both views have been criticized using theoretical and empirical arguments.
The older view has been criticized by renowned economists like Pigou and Haberler which advocated the real balance effect (also known as the Pigou effect). It has also been criticized by Friedman and other monetarists on the basis that the monetary policy has more channels through which its effects work (and thus the liquidity preference should not be taken in an absolute view). An elaborate rejection of the liquidity trap in its old and newer versions was done by Scott Sumner. Among his arguments: cash and T-bills carrying zero interest rate are not perfect substitutes. A second argument (supported by Tyler Cowen too, who underlines that Quantitative Easing is effective) is that monetary policy was actually effective during the Great Depression.
On the empirical side, as Tyler Cowen observes, even Keynes did not see any liquidity trap during the Great Depression. He also notices that, although many currently see the US in a liquidity trap, the consumer spending was rising in 2010, contrary to the predictions of the liquidity trap. On top of that, the stock market also responded in a positive manner to the Quantitative Easing measures.