Respiratory complications due to coronavirus disease COVID-19 have claimed tens of thousands of lives in 2020. Many cases of COVID-19 escalate from Severe Acute Respiratory Syndrome (SARS-CoV-2) to viral pneumonia to acute respiratory distress syndrome (ARDS) to death. Extracorporeal membranous oxygenation (ECMO) is a life-sustaining oxygenation and ventilation therapy that may be used for patients with severe ARDS when mechanical ventilation is insufficient to sustain life. While early planning and surgical cannulation for ECMO can increase survival, clinicians report the lack of a risk score hinders these efforts. In this work, we leverage machine learning techniques to develop the PEER score, used to highlight critically ill patients with viral or unspecified pneumonia at high risk of mortality or decompensation in a subpopulation eligible for ECMO. The PEER score is validated on two large, publicly available critical care databases and predicts mortality at least as well as other existing risk scores. Stratifying our cohorts into low-risk and high-risk groups, we find that the high-risk group also has a higher proportion of decompensation indicators such as vasopressor and ventilator use. Finally, the PEER score is provided in the form of a nomogram for direct calculation of patient risk, and can be used to highlight at-risk patients among critical care patients eligible for ECMO.