The sustainability of resource use and the management of public finances are both long‐run issues that are linked to each other through savings decisions. To study them conjointly, this paper introduces a public debt stabilization constraint in an overlapping generation model in which nonrenewable resources constitute a necessary input in the production function and belong to agents. It shows that stabilization of public debt at a high level (as share of capital) may prevent the existence of a sustainable development path, that is, a path on which per capita consumption is not decreasing. Public debt thus appears as a threat to sustainable development. It also shows that higher public debt‐to‐capital ratios (and public expenditures‐to‐capital ones) are associated with lower growth. Two transmission channels are identified. As usual, public debt crowds out capital accumulation. In addition, public debt tends to increase resource use which reduces the rate of growth. We also provide a numerical analysis of the dynamics that shows that the economy is characterized by saddle path stability. Finally, we show that the public debt‐to‐capital ratio may be calibrated to implement the social planner optimal allocation according to which the growth rate is increasing in the degree of patience.