The giant cholinergic interneurons of the striatum are tonically active neurons (TANs) that respond with pauses to appetitive and aversive cues, and novel events. Whereas tonic activity emerges from intrinsic properties of these neurons, glutamatergic inputs from intralaminar thalamic nuclei and dopaminergic inputs from midbrain are required for genesis of pause responses. No prior computational models encompass both intrinsic and synaptically-gated dynamics. We present a mathematical model that robustly accounts for behavior-related electrophysiological properties of TANs in terms of their intrinsic physiological properties and known afferents. In the model, balanced intrinsic hyperpolarizing and depolarizing currents engender tonic firing, and glutamatergic inputs from thalamus (and cortex) both directly excite and indirectly inhibit TANs. If this inhibition, probably mediated by GABAergic NOS interneurons, exceeds a threshold, a KIR current amplifies its effect to generate a prolonged pause. Dopamine (DA) signals modulate both TAN's intrinsic mechanisms and external inputs. Simulations revealed that many learning-dependent behaviors of TANs, including acquired pauses to task-relevant cues, are explicable without recourse to learning-dependent changes in synapses onto TANs, due to a tight coupling between DA bursts and TAN pauses. These interactions imply that reward-predicting cues often cause striatal projection neurons to receive a cascade of signals: an adaptively scaled DA burst, a brief ACh burst, and an ACh pause. A sensitivity analysis revealed a unique TAN response surface, which shows that DA inputs robustly cooperate with thalamic inputs to control cue-dependent pauses of ACh release, which strongly affects performance- and learning-related dynamics in the striatum.