How high can public debt rise without compromising fiscal solvency? We answer this question using a stochastic ability-to-pay model of sovereign default in which risk-neutral investors lend to a government that displays “fiscal fatigue,” because its ability to increase primary balances cannot keep pace with rising debt. As a result, the government faces an endogenous debt limit beyond which debt cannot be rolled-over. Using data for 23 advanced economies over 1970–2007, we find evidence of a fiscal reaction function with these features, and use it to compute “fiscal space,” defined as the difference between projected debt ratios and debt limits.