Commonly used frictional models of the labor market imply that changes in frictions have large effects on steady state employment and unemployment. We use a model that features both frictions and an operative labor supply margin to examine the robustness of this feature to the inclusion of an empirically reasonable labor supply channel. The response of unemployment to changes in frictions is similar in both models, but the labor supply response present in our model greatly attenuates the effects of frictions on steady state employment relative to the simplest matching model and two common extensions. We also find that the presence of empirically plausible frictions has virtually no impact on the response of aggregate employment to taxes.