This study adds to the extant research by investigating the differential effects of challenge‐hindrance stressors on employees' ability to meet work‐related deadlines. We also examine the mediating role of emotional exhaustion and moderating role of core self‐evaluation (CSE) in this process. Using multi‐source, time‐lagged data (N = 203) collected from employee‐supervisor dyads, this study pinpoints an important reason why employees experience of challenge and hindrance stressor invoke differential effects on their ability to meet work‐related deadlines is that they feel emotionally exhaustion when faced with stressful work demands. However, employees with high CSE can control themselves in these uncertain situations such that the indirect effects of challenge‐hindrance stressors on timely completion of work tasks, via exhaustion, are less salient for them. The study implications suggest that HR managers and decision makers need to openly communicate the risks and challenges associated with the work demands so that employees can appraise these tasks as either challenging or hindrance. Moreover, involving employees with high levels of CSE would further increase the chances that employees will complete their work tasks on time.