When taxes do not sufficiently adjust to government debt levels, the Fiscal Theory of the Price Level predicts that other variables, such as inflation and output gap, must adjust to ensure the solvency of public finances. We study the role of optimal debt maturity portfolios in this context, using a New Keynesian model with both demand and supply-side shocks. Our paper offers new analytical insights into the mechanisms through which debt maturity composition affects the trade-off between inflation and output gap: The Persistence, Discounting and Hedging channels. Our findings, based on a rich prior predictive analysis indicate that the key driving force behind optimal portfolio decisions is the Hedging channel. Moreover, the optimal maturity composition of debt is driven primarily by the supply side shocks, rather than by demand shocks. Finally, our results indicate that optimal debt management is a significant margin to complement monetary policy in stabilizing inflation when debt solvency is an important constraint.