The overlapping‐generations model of Blanchard, based on a constant probability of death, is used to study the maximum level of government debt consistent with the existence of a steady state equilibrium. In both a small open and a closed economy it is shown that maximum sustainable debt robustly occurs where the consumption of individual households reaches zero, the limit of its feasible range. Taxation absorbs all of the household's labour income here. In a closed economy, at this point the real interest rate also hits a ‘ceiling’ given by a simple combination of preference parameters and the death probability.