The ability to predict upcoming events is important to compensate for relatively long sensory-motor delays. When stimuli are temporally regular, their prediction depends on a representation of elapsed time. However, it is well known that the allocation of attention to the timing of an upcoming event alters this representation. The role of attention on the temporal processing component of prediction was investigated in a visual smooth pursuit task that was performed either in isolation or concurrently with a manual response task. Subjects used smooth pursuit eye movements to accurately track a moving target after a constant-duration delay interval. In the manual response task, subjects had to estimate the instant of target motion onset by pressing a button. The onset of anticipatory pursuit eye movements was used to quantify the subject's estimate of elapsed time. We found that onset times were delayed significantly in the presence of the concurrent manual task relative to the pursuit task in isolation. There was also a correlation between the oculomotor and manual response latencies. In the framework of Scalar Timing Theory, the results are consistent with a centralized attentional gating mechanism that allocates clock resources between smooth pursuit preparation and the parallel timing task.