Our knowledge of how circadian and homeostatic brain circuits interact to temporally organize physiology and behavior is limited. Progress has been made with the determination that lateral hypothalamic orexin (OXA) neurons control arousal and appetitive states, while suprachiasmatic nuclei (SCN) neurons function as the master circadian clock. During the day, SCN neurons exhibit heterogeneity in spontaneous resting membrane potential (RMP), with some neurons becoming severely depolarized (hyperexcited) and ceasing to fire action potentials (APs), while other neurons rest at moderate RMP and fire APs. Intriguingly, the day phase is when the SCN clock is most readily influenced by arousal, but it is unclear if and how heterogeneity in the excitability state of SCN neurons shapes their response to arousal signals, such as OXA. In whole‐cell recordings we show that during the day OXA recruits GABA‐GABAA receptor signaling to suppress the RMP of hyperexcited silent as well as moderately hyperpolarized AP‐firing SCN neurons. In the AP‐firing neurons, OXA hyperpolarized and silenced these SCN cells, while in the hyperexcited silent neurons OXA suppressed the RMP of these cells and evoked either AP‐firing, depolarized low‐amplitude membrane oscillations, or continued silence at a reduced RMP. These results demonstrate how the resting state of SCN neurons determines their response to OXA, and illustrate that the inhibitory action of this neurochemical correlate of arousal can trigger paradoxical AP firing.