The sustainability of US public debt has been widely discussed since the Great Recession. Using annual data since 1940, we estimate and compare different specifications of fiscal rules. Estimates of constant-parameter fiscal rules show no evidence of sustainability. This may be due to the instability of government's behaviour over time. Thus, we estimate a Markov-switching fiscal rule in order to identify periods of unsustainable and sustainable fiscal policies. First, we show that the government stabilizes public debt only periodically. Second, during these periods, the government's reaction is sufficiently tight to stabilize public debt over the entire horizon. We conclude that a relatively short-lived but tight fiscal contraction can be sufficient to ensure long-run US debt sustainability.