National Security Programs Authorization Act for Fiscal Years 1987 and 1988 - Title I: National Security Programs - Authorizes appropriations for the Department of Energy (DOE) for FY 1987 for plant and capital equipment and operating expenses in carrying out national security programs in the following areas: (1) weapons activities; (2) materials production; (3) defense waste and byproducts management; (4) verification and control technology; (5) nuclear safeguards and security; (6) security investigations; and (7) naval reactors development. Title II: General Provisions - Prohibits the use of funds authorized under this Act where the costs of the program exceed 105 percent of the program authorization or the costs exceed by more than $10,000,000 the amount authorized by this Act, whichever is the lesser. Prohibits the use of funds authorized by this Act for programs which have not been presented to or requested of the Congress unless the Secretary of Energy transmits to the appropriate committees a full and complete statement of the action proposed. Authorizes the Secretary to carry out any general plant project only if the maximum estimated cost of the project does not exceed $1,200,000. Sets forth procedures for the approval of projects which exceed by more than 25 percent their estimated cost, and exempts from such procedures any project which has an estimated cost of less than $5,000,000. Allows the transfer of funds from specified projects to other Government agencies for the performance of work for which the appropriation is made. Authorizes the Secretary to perform construction design services for construction projects in support of national security programs. Permits funds to remain available until expended if so specified in an appropriation Act. Title III: Authorization of Appropriations For Fiscal Year 1988 - Authorizes appropriations for programs under this Act for FY 1988 to DOE, such funds not to be available before FY 1988.