It is well known that the requirement to perform a concurrent task interferes with many aspects of perception and cognition. Evidence suggests that this interference extends to spatial shifts of attention, which appear to be reduced in efficiency when they must be performed while processing related to another task is ongoing. Here, the authors investigate whether concurrent tasks also interfere with shifts of temporal attention—that is, with the ability to shift attention to an expected time of stimulus onset. In Experiment 1, using the attentional blink paradigm, the authors show that the requirement to identify a prior target interferes with observer’s ability to shift attention to the expected time of second-target onset. In Experiments 2 and 3, they confirm the role of the first-target task by eliminating the shifting deficit when the interval between the targets is increased or the requirement to identify the first target is removed. Together, the results indicate that performing a concurrent task interferes with temporal shifts of attention analogously to how it interferes with spatial shifts of attention, implying an impact of task-related resource limitations on a common set of underlying cognitive and perceptual mechanisms.