This paper inspects the 'deep' habits mechanism originally used by Ravn, Schmitt-Grohé and Uribe (2006) to generate the positive comovement of public and private consumption observed in many VAR studies. In their set-up, the price-elasticity of demand is pro-cyclical and it is optimal for the firm to lower the mark-up while expanding production after the fiscal shock, raising the demand for labor and the real wage. Consequently, agents substitute consumption for leisure and overcome the negative wealth effect of the fiscal expansion. Here, we show that increasing price stickiness reduces the impact of the fiscal shock on the real wage and hinders the rise of consumption. If the degree of price stickiness is high enough, consumption is crowded-out. This is in contrast to the role of price rigidities in the standard New Keynesian model where they weaken the crowding-out of consumption.