This study integrates network and content analyses to examine exposure to cross-ideological political views on Twitter. We mapped the Twitter networks of 10 controversial political topics, discovered clusters - subgroups of highly self-connected users - and coded messages and links in them for political orientation. We found that Twitter users are unlikely to be exposed to cross-ideological content from the clusters of users they followed, as these were usually politically homogeneous. Links pointed at grassroots web pages e.g.: blogs more frequently than traditional media websites. Liberal messages, however, were more likely to link to traditional media. Last, we found that more specific topics of controversy had both conservative and liberal clusters, while in broader topics, dominant clusters reflected conservative sentiment.