We investigate what happens when the fiscal authorities do not react to rising public debt so that the unpleasant task of fiscal sustainability falls upon the Central Bank (CB). In particular, we explore whether the CB's bond purchases in the secondary market can restore stability and determinacy in an otherwise unstable economy. This is investigated in a dynamic general equilibrium model calibrated to the Euro Area (EA) and where monetary policy is conducted subject to the numerical rules of the Eurosystem (ES). We show that given the recent situation in the ES, and to the extent that a relatively big shock hits the economy, there is no room left for further quasi-fiscal actions by the ECB; there will be room only if the ES' rules are violated. We then search for policy mixes that can respect the ES's rules and show that debt-contingent fiscal and quantitative monetary policies can reinforce each other; this confirms the importance of policy complementarities.