Some people still seem unable, or maybe unwilling, to understand the basic New Keynesian (NK) model. Should it be surprising in this model that cutting taxes on wages at the Zero Lower Bound (i.e. when nominal interest rates are fixed) are contractionary? Of course not. The basic NK model contains an intertemporal consumption function that implies Ricardian Equivalence holds, so consumers save all of the extra income they get from a tax cut. But cutting taxes increases the incentive to work, thereby increasing labour supply, which through a Phillips curve decreases inflation. With a fixed nominal interest rate that implies higher real rates, which are contractionary. QED.
Now the main thing not to like here is the consumption function and Ricardian Equivalence. Empirical evidence points strongly to a significant income effect, with a marginal propensity to consume around a third rather than zero. There are good theoretical reasons why you might get this result, even with totally rational consumers. But the implication that cutting taxes will lead to some increase in labour supply seems reasonable, and that will put some downward pressure on inflation. This is why pushing ‘structural reforms’ that expand the supply side in a liquidity trap can be counterproductive in the short term. (Things are more complex when you have a fixed exchange rate.)
Now you may quite reasonably believe that in the real world a positive income effect from a tax cut will raise demand by more than any increase in supply, so inflation will rise and real rates will fall. But it remains the case that as a stimulus measure directly raising demand through higher government spending does not generate this supply side offset. That the NK model has this feature seems like a virtue to me. The only point I have to add is that because helicopter money, as traditionally envisaged, is a lump sum transfer (everyone gets an equal amount, so it is independent of wages), you do not get this offsetting supply side effect. So for that reason helicopter money is more effective as a stimulus instrument in a liquidity trap than cutting taxes on wages.