....an opportunity to experience science and technology (S&T) policy firsthand while working closely with senior policymakers on a variety of tasks and projects. OSTP provides the President with S&T analysis and judgment in regards to major policies, plans, and programs of the Federal government. In addition, the Office leads an interagency effort to develop and implement sound S&T policies and budgets in the Federal enterprise. OSTP works with the private sector to ensure Federal S&T investments contribute to economic prosperity, environmental quality, and security of the Nation.Please visit http://www.whitehouse.gov/administration/eop/ostp/about/student/ for details.
It appears these internships are available spring, summer or fall, 90 days maximum and are open to undergraduate and graduate students (must be enrolled at the time of participation). Currently, the spring 2012 application deadline is posted (Nov. 4) but there is no information on their summer application deadline.
This is not the White House interns program (but the above link has a link to that program).