People express and amplify political opinions in Microblogs such as Twitter, especially when major political decisions are made. Twitter provides a useful vehicle for capturing and tracking popular opinion on burning issues of the day. In this paper, we focus on tracking the changes in political sentiment related to the U.S. Supreme Court (SCOTUS) and its decisions, focusing on the key dimensions on support, emotional intensity, and polarity. Measuring changes in these sentiment dimensions could be useful for social and political scientists, policy makers, and the public. This preliminary work adapts existing sentiment analysis techniques to these new dimensions and the specifics of the corpus (Twitter). We illustrate the promise of our work with an important case study of tracking sentiment change building up to, and immediately following one recent landmark Supreme Court decision. This example illustrates how our work could help answer fundamental research questions in political science about the nature of Supreme Court power and its capacity to influence public discourse.