"Mission-oriented" public research organizations invest in R&D to improve decision-making around complex policy problems from climate change to asteroid impacts, thus producing public value. However, the estimation of benefits produced by such R&D projects is notoriously difficult to predict and measure - a challenge that is magnified for global catastrophic risks (GCRs). GCRs are highly uncertain risks that may pose enormous negative consequences for humanity. This article explores how public research organizations systematically reduce key uncertainties associated with GCRs. Building off of recent literature highlighting the organizational and political factors that influence R&D priority-setting at public research organizations, this article develops an analytical framework for explaining R&D priority-setting outcomes that integrates the key stages of decision analysis with organizational and political dynamics identified in the literature. This framework is then illustrated with a case study of the NASA Planetary Defense Coordination Office, which addresses the GCR of near-Earth object (asteroid and comet) impacts. The case study reveals how organizational and political factors interact with every stage in the R&D priority-setting process - from initial problem definition to project selection. Lastly, the article discusses the extent to which the case study can inform R&D priority-setting at other public organizations, particularly those addressing GCRs.