As a global pandemic, COVID‐19 impacts work‐related processes, placing strain upon many employees in project teams. Identifying process variables and potential organizational resources can play an important role in addressing employee mental health, both for the current pandemic and future crises. Based on an extension of the job demands–resources model, this paper introduces COVID‐19 demands as distal job demands, examining their influence on emotional exhaustion through proximal unfinished tasks. Furthermore, we suggest that agile project management acts as a buffering job resource in this relationship. In two studies, we drew samples from Germany (N = 168) and the USA (N = 292). Across studies, COVID‐19 demands had an indirect effect on emotional exhaustion, mediated by unfinished tasks. Furthermore, agile project management acts as a buffering job resource for individuals in Germany, attenuating the relationship between COVID‐19 demands, unfinished tasks and subsequent feelings of emotional exhaustion. In contrast, findings from Study 2 revealed that COVID‐19 demands were more strongly related to unfinished tasks and subsequent feelings of emotional exhaustion in the USA when individuals reported higher levels of agile project management. Taken together, our results indicate that project work under COVID‐19 fosters feelings of emotional exhaustion through the accumulation of unfinished tasks.