This paper compares the results of two surveys that characterize attitudes about the institutional archives of two forms of public social media, Twitter tweets (i.e. microblog posts) and Flickr photos (i.e. shared visual media). Internet-savvy respondents were asked to assess three statements about a hypothetical scenario in which the Library of Congress archived and provided access to the social media in question. Access to the archives varied in three ways: (1) the public was given immediate access to the archive; (2) researchers were given immediate access to the archive; and (3) the public was given deferred access (by 50 years) to the archive. We found that access to photos was received best when it was deferred by 50 years, and access to tweets was received best when it was limited to researchers, hence suggesting that institutions pay careful attention to access limitations when they are seeking public acceptance of their archiving efforts.