This paper analyzes the impact of monetary policy constraints and environment on public debt sustainability through the lens of a general equilibrium model of fiscal limits à la Bi (2012). We find that the mere possibility of a binding ZLB has a detrimental impact on debt sustainability, with a new peak of the Laffer curve corresponding to lower tax revenues and higher interest rates. This induces a dead-weight loss in the present discounted value of future primary surpluses, compared to an unconstrained economy. Moreover, we find that debt sustainability increases with monetary policy activeness, that is, with the elasticity of the interest rate to changes in inflation and the output gap. This result is mainly due to the lower fiscal costs stemming from mitigated inflation fluctuations. On this basis, we assess the trade-off between economic stabilization and debt sustainability faced by the government depending on the monetary policy environment. In normal times, large public spending shocks may engender perverse debt dynamics and eventually cause economic contractions. At the ZLB, a muted trade-off between stabilization and sustainability instead expands the fiscal margin for such shocks, especially if coupled with a commitment to a more active monetary policy during normal times.