We study the mechanism by which unconventional (balance-sheet) monetary policy can rule out self-fulfilling sovereign default in a model with optimizing but discretionary fiscal and monetary policymakers. By purchasing sovereign debt, the central bank effectively swaps risky government paper for monetary liabilities only exposed to inflation risk, thus yielding a lower interest rate. We characterize a critical threshold for central bank purchases beyond which, absent fundamental fiscal stress, the government strictly prefers primary surplus adjustment to default. Since default may still occur for fundamental reasons, however, the central bank faces the risk of losses on sovereign debt holdings, which may generate inefficient inflation. This risk does not undermine the credibility of a backstop, nor the ability of a central bank to pursue its inflation objectives when the latter enjoys fiscal backing or fiscal authorities are sufficiently averse to inflation.