President Lyndon Baines Johnson’s presidential library has holdings relevant to the study of federal education policy history, such as these Douglass Cater oral histories. Cater served as special assistant to the President from 1964 to 1968, and offered comments on the politics of education at the time of enactment of the Elementary and Secondary Education Act of 1965.
The U.S. Department of Education’s National Education Library in Washington, DC has a wealth of resources on federal education policy history:
So too does the Library of Congress (also in Washington, DC). It is a particularly good place to go for copies of congressional hearings, prints, and other legislative documents.
Google Books also is a place where one can find old studies of the federal role in education.
University Microfilms International has copies of dissertations completed at U.S. colleges and universities since 1860. Many, many dissertations have focused on federal education policy and politics. You can search them online through Proquest, provided you have a subscription or are at a research library.