We study supply and demand shocks in a disaggregated model with multiple sectors, multiple factors, input-output linkages, downward nominal wage rigidities, credit-constraints, and a zero lower bound. We use the model to understand how the COVID-19 crisis, an omnibus supply and demand shock, affects output, unemployment, and inflation, and leads to the coexistence of tight and slack labor markets. We show that negative sectoral supply shocks are stagflationary, whereas negative demand shocks are deflationary, even though both can cause Keynesian unemployment. Furthermore, complementarities in production amplify Keynesian spillovers from supply shocks but mitigate them for demand shocks. This means that complementarities reduce the effectiveness of aggregate demand stimulus. In a stylized quantitative model of the United States, we find supply and demand shocks each explain about one-half of the reduction in real GDP from February to May 2020. Although there was as much as 6 percent Keynesian unemployment, this was concentrated in certain markets. Hence, aggregate demand stimulus is one quarter as effective as in a typical recession where all labor markets are slack. (JEL E12, E23, E24, E31, E32, E62, I12)