Sovereign debt crises coincide with deep recessions. I propose a model of sovereign debt that rationalizes large contractions in economic activity via an aggregate-demand amplification mechanism. The mechanism also sheds new light on the response of consumption to sovereign risk, which I document in the context of the Eurozone crisis. By explicitly separating the decisions of households and the government, I examine the interaction between sovereign risk and precautionary savings. When a default is likely, households anticipate its negative consequences and cut consumption for self-insurance reasons. Such shortages in aggregate spending worsen economic conditions through nominal wage rigidities and boost default incentives, restarting the vicious cycle. I calibrate the model to Spain in the 2000s and find that about half of the output contraction is caused by default risk. More generally, sovereign risk exacerbates volatility in consumption over time and across agents, creating large and unequal welfare costs even if default does not materialize.