We build a medium-scale DSGE model and calibrate it to fit the main macroeconomic variables during the US Great Recession. Using it to evaluate the welfare effects of increasing government consumption at the zero lower bound beyond what actually observed in the data, we reach three main results. First, the increase in government consumption after 2008, albeit small in present value terms, was close to optimal. Second, frontloading the same stimulus would have been welfare-improving. Third, larger welfare effects occur in our model for parameter values implying either large welfare costs of modest recessions (e.g. high consumption curvature), or large recessions.