We construct a model of a monetary union to study fiscal consolidation in the periphery of the euro area, through cuts in public sector wages or hiring when the nominal interest rate is constrained at its lower bound. Consolidation induces a positive wealth effect that increases demand, as well as a reallocation of workers towards the private sector, which together boost private activity. However, in a low-inflation environment, demand is suppressed and the private sector is not able to absorb the additional workers. Comparing the two instruments, cuts in public hiring increase unemployment persistently in this environment, while wage cuts can reduce it. Regions with higher mobility of labor between the two sectors are able to consolidate more effectively. Price flexibility is also key at the zero lower bound: for a higher degree of price rigidity in the periphery, consolidation becomes harder to achieve. Consolidations can be self-defeating when the public good is productive.