Background: As the SARS-CoV-2 Omicron variant emerged and spread globally at an alarming speed, healthcare workers’ (HCWs) uncertainties, worries, resilience, and coping strategies warranted assessment. The COVID-19 pandemic had a severe psychological impact on HCWs, including the development of Post-Traumatic Stress symptoms. Specific subgroups of HCWs, such as front-line and female workers, were more prone to poor mental health outcomes and difficulties facing stress. Methods: The responses to an online questionnaire among HCWs in the Kingdom of Saudi Arabia (KSA) were collected from 1 December 2021 to 6 December 2021, aiming to assess their uncertainties, worries, resilience, and coping strategies regarding the Omicron variant. Three validated instruments were used to achieve the study’s goals: the Brief Resilient Coping Scale (BRCS), the Standard Stress Scale (SSS), and the Intolerance of Uncertainty Scale (IUS)—Short Form. Results: The online survey was completed by 1285 HCWs. Females made up the majority of the participants (64%). A total of 1285 HCW’s completed the online survey from all regions in KSA. Resilient coping scored by the BRCS was negatively and significantly correlated with stress as scored by the SSS (r = −0.313, p < 0.010). Moreover, intolerance of uncertainty scored by the IUS positively and significantly correlated with stress (r = 0.326, p < 0.010). Increased stress levels were linked to a considerable drop in resilient coping scores. Furthermore, being a Saudi HCW or a nurse was linked to a significant reduction in resilient coping ratings. Coping by following healthcare authorities’ preventative instructions and using the WHO website as a source of information was linked to a considerable rise in resilient coping. Conclusions: The negative association between resilient coping and stress was clearly shown, as well as how underlying intolerance of uncertainty is linked to higher stress among HCWs quickly following the development of a new infectious threat. The study provides early insights into developing and promoting coping strategies for emerging SARS-CoV-2 variants.