The COVID-19 pandemic is a global crisis that has been testing every society and exposing the critical role of local politics in crisis response. In the United States, there has been a strong partisan divide between the Democratic and Republican party's narratives about the pandemic which resulted in polarization of individual behaviors and divergent policy adoption across regions. As shown in this case, as well as in most major social issues, strongly polarized narrative frameworks facilitate such narratives. To understand polarization and other social chasms, it is critical to dissect these diverging narratives. Here, taking the Democratic and Republican political social media posts about the pandemic as a case study, we demonstrate that a combination of computational methods can provide useful insights into the different contexts, framing, and characters and relationships that construct their narrative frameworks which individual posts source from. Leveraging a dataset of tweets from elite politicians in the U.S., we found that the Democrats' narrative tends to be more concerned with the pandemic as well as financial and social support, while the Republicans discuss more about other political entities such as China. We then perform an automatic framing analysis to characterize the ways in which they frame their narratives, where we found that the Democrats emphasize the government's role in responding to the pandemic, and the Republicans emphasize the roles of individuals and support for small businesses. Finally, we present a semantic role analysis that uncovers the important characters and relationships in their narratives as well as how they facilitate a membership categorization process. Our findings concretely expose the gaps in the "elusive consensus" between the two parties. Our methodologies may be applied to computationally study narratives in various domains.