Recent physiological studies using behaving monkeys revealed that, in a two-alternative forced-choice visual motion discrimination task, reaction time was correlated with ramping of spike activity of lateral intraparietal cortical neurons. The ramping activity appears to reflect temporal accumulation, on a timescale of hundreds of milliseconds, of sensory evidence before a decision is reached. To elucidate the cellular and circuit basis of such integration times, we developed and investigated a simplified two-variable version of a biophysically realistic cortical network model of decision making. In this model, slow time integration can be achieved robustly if excitatory reverberation is primarily mediated by NMDA receptors; our model with only fast AMPA receptors at recurrent synapses produces decision times that are not comparable with experimental observations. Moreover, we found two distinct modes of network behavior, in which decision computation by winner-take-all competition is instantiated with or without attractor states for working memory. Decision process is closely linked to the local dynamics, in the "decision space" of the system, in the vicinity of an unstable saddle steady state that separates the basins of attraction for the two alternative choices. This picture provides a rigorous and quantitative explanation for the dependence of performance and response time on the degree of task difficulty, and the reason for which reaction times are longer in error trials than in correct trials as observed in the monkey experiment. Our reduced two-variable neural model offers a simple yet biophysically plausible framework for studying perceptual decision making in general.