Politicians are increasingly using social media platforms, specifically the microblog Twitter, to interact with the public and express their stances on current policy issues. Due to this nearly one-on-one communication between politician and citizen, it is imperative to develop automatic tools for analyzing how politicians express their stances and frame issues in order to understand how they influence the public. Prior to my work, researchers have focused on supervised, linguistic-based approaches for the prediction of stance or agreement of the content of tweets and classification of the frames and moral foundations used to express a single tweet. The generalizability of these approaches, however, is limited by the need for direct supervision, dependency on current language, and lack of use of social and behavioral context available on Twitter. My works are among the first to study these general political strategies specifically for politicians on Twitter. This requires techniques capable of abstracting the textual content of multiple tweets in order to generalize across politicians, specific policy issues, and time. In this dissertation, I propose breaking from traditional linguistic baselines to leverage the rich social and behavioral features present in tweets and the Twitter network as a form of weak supervision for studying political discourse strategies on microblogs. My approach designs weakly supervised models for the identification, extraction, and modeling of the relevant linguistic, social, and behavioral patterns of Twitter. These models help shed light on the interconnection of ideological stances, framing strategies, and moral viewpoints which underlie the relationship between a politician's behavior on social media and in the real world.