Political discourse on social media often contains similar language with opposing intended meanings. For example, the phrase thoughts and prayers, is used to express sympathy for mass shooting victims, as well as satirically criticize the lack of legislative action on gun control. Understanding such discourse fully by reading only the text is difficult. However, knowledge of the social context information makes it easier. We characterize the social context required to fully understand such ambiguous discourse, by grounding the text in real-world entities, actions, and attitudes. We propose two datasets that require understanding social context and benchmark them using large pre-trained language models and several novel structured models. We show that structured models, explicitly modeling social context, outperform larger models on both tasks, but still lag significantly behind human performance. Finally, we perform an extensive analysis, to obtain further insights into the language understanding challenges posed by our social grounding tasks.