Framing is a political strategy in which politicians carefully word their statements in order to control public perception and discussion of current issues. Previous works exploring political framing have focused on analysis of frames in longer texts, such as newspaper articles, or tweets relevant to specific events. We present the first in-depth analysis of issue-independent framing for political discourse in social media, specifically the microblogging platform Twitter. Building upon the fifteen frames designed by Boydstun, we propose three additional frames relevant to Twitter and provide insights into the dynamic usage of frames by party and over time. Finally we present a global probabilistic model for combining linguistic, issue, and party bias features of the tweets of politicians for the task of tweet frame prediction.