This paper offers a formal analysis of the relationship between changes in government primary balance and debt-to-GDP ratio. It establishes the conditions under which a fiscal consolidation increases, instead of decreasing, the stock of government liabilities relative to aggregate output.A crucial role is played by the relationship between the elasticities of average cost of debt and nominal output to primary balance. While the former depends on debt maturity and risk premia-dynamics, the latter relates to the well-known controversy on the size of government spending multipliers. The paper shows an application to the ongoing fiscal consolidation process in the Eurozone.