General Social Survey (GSS)
The GSS measures public opinion in the United States on a wide variety of topics of interest to social scientists. The survey, which began in the early 1970's, provides a biennial perspective on American attitudes toward government, life, race, religion, and other social issues. The link here is to the GSS homepage within the National Opinion Research Center. Sites where researchers can extract and download specific variables of interest are listed here. The SDA Archive at Berkeley also holds GSS data from 1972 to 2016 in an interface that allows for basic on-line data analysis and the creation of subsets of GSS data. GSS data are also available via the Roper Center.
The Policy Mood data, which have been assembled by James A. Stimson and K. Elizabeth Coggins at UNC-Chapel Hill, " is a time series measure of public support for government programs on the liberal-conservative continuum." The data cover the years 1952 onwards. An issue-specific variant of the Policy Mood data is available via the Policy Agendas Project (see above). Mood data are also available via James Stimson's page at UNC.
Roper Center for Public Opinion Research
The Roper Center is one of the country's premier centers for polling data, with holdings dating back to 1935. While the bulk of the Center's data are for national polls, it also includes many state-level polls as well. The iPOLL interface may be of particular use because it allows users to search through surveys at the question level. Roper also has a large compilation of Presidential approval ratings. The Roper Center is also available via Databases at Emory.