In the whisker-barrel system, layer IV excitatory neurons respond preferentially to high-velocity deflections of their principal whisker, and these responses are inhibited by deflections of adjacent whiskers. Thalamic input neurons are amplitude and velocity sensitive and have larger excitatory and weaker inhibitory receptive fields than cortical neurons. Computational models based on known features of barrel circuitry capture these and other differences between thalamic and cortical neuron response properties. The models' responses are highly sensitive to thalamic firing synchrony, a finding subsequently confirmed in real barrels by in vivo experiments. Here, we use dynamic systems analysis to examine how barrel circuitry attains its sensitivity to input timing, and how this sensitivity explains the transformation of receptive fields between thalamus and cortex. We find that strong inhibition renders the net effect of intracortical connections suppressive or damping, distinguishing it from previous amplifying models of cortical microcircuits. In damping circuits, recurrent excitation enhances response tuning not by amplifying responses to preferred inputs, but by enabling them to better withstand strong inhibitory influences. Dense interconnections among barrel neurons result in considerable response homogeneity. Neurons outside the barrel layer respond more heterogeneously, possibly reflecting diverse networks and multiple transformations within the cortical output layers.