Growing evidence from primate neurophysiology and modeling indicates that in reaction time tasks, a perceptual choice is made when the firing rate of a selective cortical neural population reaches a threshold. This raises two questions: what is the neural substrate of the threshold and how can it be adaptively tuned according to behavioral demands? Using a biophysically based network model of spiking neurons, we show that local dynamics in the superior colliculus gives rise to an all-or-none burst response that signals threshold crossing in upstream cortical neurons. Furthermore, the threshold level depends only weakly on the efficacy of the cortico-collicular pathway. In contrast, the threshold and the rate of reward harvest are sensitive to, and hence can be optimally tuned by, the strength of cortico-striatal synapses, which are known to be modifiable by dopamine-dependent plasticity. Our model provides a framework to describe the main computational steps in a reaction time task and suggests that separate brain pathways are critical to the detection and adjustment of a decision threshold.