Processing of external stimuli by cortical network has been described using the "balanced state" idea, stating that the average external input, excitation and inhibition to cortical neuron balance each other in the leading order. As a result, neuronal firing properties are determined by fluctuations in the input. It is unclear, however, whether real cortical circuits receive enough synaptic inputs to allow this scenario to happen. We study a model of a network in the somatosensory system of a mouse composed of 1600 excitatory and 100 inhibitory neurons that receive excitatory inputs from 200 thalamic neurons. Those thalamic neurons convey information about movement of whiskers ("whisking") and their touch with objects. Each cortical neuron is innervated, at random, from about 100 thalamic neurons. We find that the large overlap between the inputs induces synchrony among neurons. Despite this fact, the firing properties of the neuronal populations follow qualitatively the prediction of the analytical theory. For example, the firing rates of the two population increases linearly with the input strength, and the coefficient of variation CV is somewhat below 1. In response to touch signals, however, the firing activity is governed by transient responses to contact.