This paper introduces a public debt stabilization constraint in an overlapping generation model in which non-renewable resources constitute a necessary input in the production function and belong to agents. It shows that stabilization of public debt at high level (as share of capital) may prevent the existence of a sustainable development path. 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 show 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.