This paper studies the interplay between deadlines and cognitive limitations. We analyze an agent's decision to complete a one-off task under a deadline. Postponing the task can be beneficial for the agent; missing the deadline, however, leads to a drop in the agent's rewards. If the agent exhibits cognitive limitations, postponing increases the risk of becoming inattentive and failing to complete the task in time. Our framework provides a rich set of predictions on the behavioral implications of deadlines. We test these predictions in a field experiment at a dental clinic, in which we exogenously vary deadlines and rewards for arranging check-up appointments. The empirical results underline the behavioral relevance of cognitive limitations. Imposing relatively tight deadlines induces patients to act earlier and at a persistently higher frequency than without a deadline. Evidence from a follow-up experiment and complementary surveys supports the notion that deadlines may serve as a powerful instrument when individuals' cognitive capacity is limited.