We identify an adverse consequence of natural resource windfalls, which is particularly detrimental in advanced democracies. We construct a political economy model with endogenous public debt under exogenous resource windfall shocks, in which political myopia results from reelection prospects. Reelection-seeking politicians, while more accountable toward their electorate, are also more myopic. The latter effect gives rise to a budget deficit bias, with the ensuing debt buildup that is exacerbated by resource windfalls. We find that the positive effect of resource windfalls on debt increases as the restrictions on reelection get laxer. We test the model's predictions using a panel of U.S. states over the period 1963-2007. Our identification strategy rests on constitutionally-entrenched differences in gubernatorial term limits that provide plausibly exogenous cross-sectional and time variation in political time horizon, and geographically-based cross-state differences in natural endowments interacted with the international prices of oil and gas. The empirical findings corroborate the model's predictions. In particular, over a period of five years, a resource windfall equivalent to 1% of state income induces an increase of approximately 0.35% ($4.6) in the average real per capita public debt of states with no gubernatorial term limits.