Social media records the thoughts and activities of countless cultures and subcultures around the globe. Yet institutional efforts to archive social media content remain controversial. We report on 988 responses across six surveys of social media users that included questions to explore this controversy. The quantitative and qualitative results show that the way people think about the issue depends on how personal and ephemeral they view the content to be. They use concepts such as creator privacy, content characteristics, technological capabilities, perceived legal rights, and intrinsic social good to reason about the boundaries of institutional social media archiving efforts.