The COVID-19 pandemic started at the end of 2019 and can be considered one of the most difficult health crises of the past century. It has had a devastating effect around the world, not only for public health, but also for the economy, labor market, and other facets of individual and societal life. Health systems have been put under high strain, and health professionals have experienced unusual and stressful work circumstances. With the aim of drawing lessons for nursing education, the present study analyzed, during the weeks of peak infection in Spain, the stress experience and coping strategies of a sample of 403 nurses from the Spanish health system. Specifically, we analyzed how tenure, stress appraisal, problem-focused coping, and support-seeking coping predicted nurses’ awareness of their education needs, both in terms of technical-professional knowledge and skills and transversal skills. Structural equation modeling analysis revealed that more tenure (years of experience) was related to lower stress appraisal (workload, −0.12, p < 0.05; insufficient preparation, −0.33, p < 0.001; and fear of contagion −0.36, p < 0.001) and more problem focused coping (PFC) strategies were related to higher awareness of professional (0.18, p < 0.01) and transversal educational needs (0.17, p < 0.01) while support seeking strategies just related to transversal training needs (0.10, p < 0.05). Moreover, the participants provided valuable input about specific contents to be considered in future nursing education programs. Implications for redesigning the nursing degree curriculum are analyzed in the discussion section.