In this study, I examined cognitive structures consisting of frames that people used in the open-ended responses to a survey question about cuts in welfare benefits. The study shows that patterns of individuals' entertainment and news media use are important sources of frames that people adopt in thinking about an important public issue. In turn, those frames partly derived from the media shape the public's policy preferences beyond controls for individuals' social location, ideology, interpersonal communication, and knowledge. Frames that are related to particular patterns of media use (e.g., increase in differences between poor and rich, need for specific approaches, some will go hungry) have power to alter even deep, ideologically motivated welfare preferences. However, the results suggest that the media's most important role may be in spreading out the field of thinkable solutions to public problems rather than making any particular position dominant in policy decision making.