We study supply and demand shocks in a general disaggregated model with multiple sectors, factors, and input-output linkages, as well as downward nominal wage rigidities and a zero lower bound constraint. We use the model to understand how the Covid-19 crisis, an omnibus of supply and demand shocks, affects output, unemployment, and inflation, and how it leads to the coexistence of tight and slack labor markets. Under some conditions, the details of the production network can be summarized by simple sufficient statistics. We use these sufficient statistics to conduct global comparative statics. Negative sectoral supply shocks and sectoral demand shocks are stagflationary, whereas negative intertemporal demand shocks are deflationary. Complementarities magnify Keynesian spillovers for the former shocks but mitigate them for the latter. We illustrate the intuition using a nonlinear AS-AD representation. In a quantitative model of the US calibrated to current disaggregated data, sectoral supply and demand shocks on their own generate more than 10% inflation, and negative intertemporal demand shocks on their own generate 7% deflation. Both types of shocks are necessary to capture the disaggregated data, each explains about half the reduction in real GDP, and putting both together results in 0.3% inflation and as much as 8.5% Keynesian unemployment in April 2020. Nevertheless, aggregate demand stimulus is only about a third as effective as in a typical recession where all labor markets are slack. More targeted forms of demand stimulus are more effective.