Unstable government debt dynamics can typically be stabilized around a certain target level of debt by adjustments in various fiscal instruments, like government spending, transfers, or taxes. This paper investigates properties of debt stabilizing rules which link the needed budgetary adjustments to the state of the economy. The paper establishes that the magnitude of the target level of long-run debt is a key determinant of whether it is possible to find a rule of this type that can be implemented under all available fiscal instruments. Specifically, considering linear feedback rules, the paper demonstrates that there may well exist a critical target level of debt beyond which this is no longer possible. From an applied perspective, this finding is of particular relevance in the context of a monetary union with decentralized fiscal policies. Depending on the target level of debt, there might be a conflict between a common fiscal framework that tracks deficit developments as a function of the state of the economy and the unrestricted choice of fiscal policy instruments at the national level.