We investigate the link between the size of government indebtedness and the effectiveness of government spending shocks in normal times and at the Zero Lower Bound (ZLB). We develop a New Keynesian model with capital, distortionary taxes and public debt in which the ZLB constraint on the nominal interest rate may be binding. In normal times, high steady-state levels of government debt to GDP lead to reduced output multipliers. After a negative capital quality shock that pushes the economy at the ZLB however, high steadystate debt levels produce larger output multipliers. Our results rely on the fact that fiscal policy becomes self-financing at the ZLB, and that distortionary taxes rise (respectively fall) after a spending shock at the steady state (resp. ZLB). Our results have non-trivial consequences on the design of optimized spending policies in the event of large economic downturns.