The worldwide pandemic that started in December 2019 was a cause of a great rise in the feeling of threat in society. A feeling of threat and distress can be influenced by the span of emotions experienced by a person, and as it is rather clear, that the situation of pandemic evokes negative emotions, they can range from fear to depression, to even disgust. In this study, we wanted to verify the influence of the negative emotions of automatic origin, related to the well-being and homeostasis of the organism and the negative emotions of reflective origin, which are related to social constructs, on the feeling of threat caused by the pandemic outbreak. We expected automatic emotions to have a greater influence on the feeling of threat. We used an online questionnaire to measure the intensity of negative emotions and the feeling of threat among Polish participants in the time of the early outbreak of the pandemic (March–April 2020). Regression analyses were used to identify the predictors of the feeling of threat. The results show the distinctive effect of automatic and reflective groups of emotions. While automatic emotions always increased the feeling of threat, the reflective emotions suppressed the distress, especially in the group of middle-aged and elderly participants. As reflective emotions are developing in the process of socialization, the observed results could suggest, that young people do not process the situation of the pandemic in reflective categories, which leaves them more worried about the situation. We suggest, that promoting reflective thinking can be helpful in interventions in the cases of anxiety caused by the pandemic, as well as in social communication regarding the topic of the pandemic.