We argue that the fiscal multiplier of government purchases is increasing in the spending shock, in contrast to what is assumed in most of the literature. The fiscal multiplier is largest for large positive government spending shocks and smallest for large contractions in government spending. We empirically document this fact using aggregate U.S. data. We find that a neoclassical, life-cycle, incomplete markets model calibrated to match key features of the US economy can explain this empirical finding. The mechanism hinges on the relationship between fiscal shocks, their form of financing, and the response of labor supply across the wealth distribution. The model predicts that the aggregate labor supply elasticity is increasing in the size of the fiscal shock, and this holds regardless of whether shocks are deficit- or balanced-budget financed (albeit through different mechanisms). We find evidence of our mechanism in micro data for the US.