We develop a New Keynesian model augmented with a rich description of fiscal policy, including debt maturity structure, where two policymakers - an independent inflation-averse central bank and a (potentially) populist fiscal authority – interact strategically. Central bank independence initially improves inflation outcomes, but this results in reduced fiscal discipline and increased debt. Eventually this leads to inflation lying above pre‑independence levels. Introducing a ‘flight-to-safety’ regime, which suppresses the interest rates households require to hold government debt, and a conventional regime, where their time preferences return to normal, allows us to explore how changes in the natural rate can dramatically affect debt dynamics and inflation outcomes. The model offers an explanation of the buildup of government debt since the financial crisis and the subsequent emergence of significant inflation.