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This paper analyses the risk of default on public debt within a repeated game between the governement and private investors. The government has only an imperfect control over the stream of future revenues. In this case, a long sequence of adverse budgetary shocks may push the debt over its sustainable level, defined as the discounted flow of future primary surpluses. Given this small risk of unsustainability, we put forward a debt threshold above which investors refuse to subscribe to a new debt issue. But this shortage of liquidity suffices to bring about default. Hence, this “illiquidity” threshold becomes the new critical threshold. The series of decreasing critical illiquidity thresholds converges to a limit value. This risk-free debt level may be much lower than the sustainable level. Policy implications call for a more restrictive definition of a sound fiscal stance.Classification JEL: E62, F34, H63