Humans were trained on a temporal discrimination to make one response when the stimulus duration was short (2 s) and a different response when the stimulus duration was long (8 s). They were then tested with stimulus durations in between to determine the bisection point. In Experiment 1, we examined the effect of a secondary cognitive task (counting backwards by threes) on the bisection point when participants were trained without a cognitive load and were tested with a cognitive load or the reverse (relative to appropriate controls). When the cognitive load increased from training, the psychophysical function plotting long responses against the increase in stimulus duration shifted to the right (as if the internal clock slowed down), and when the cognitive load decreased from training the psychophysical function shifted to the left (as if the internal clock speeded up). In Experiment 2, when the secondary task consisted of exerting continuous force on a transducer (a physically effortful task), it had the opposite effect. When the required force increased from training, the psychophysical function shifted to the left (as if the internal clock speeded up), and when the required force decreased from training, the psychophysical function shifted to the right (as if the internal clock slowed down). The results support an attentional view of the subjective passage of time. A cognitive secondary task appears to decrease attention to temporal cues, resulting in the underestimation of the passage of time, whereas a force requirement appears to increase attention to temporal cues, resulting in the overestimation of the passage of time.