Federal Procurement and Assistance Integrity Act - States that the purpose of this Act is to improve the efficiency and effectiveness and protect the integrity of the Federal procurement and assistance systems by ensuring that the Federal Government does business with responsible contractors and participants. (Sec. 3) Authorizes the Secretary of Labor to debar or suspend a person from procurement or nonprocurement activities upon a finding, in accordance with procedures developed under this Act, that the person violated any of the following: (1) the National Labor Relations Act; (2) the Fair Labor Standards Act; (3) the Occupational Safety and Health Act; or (4) Federal requirements for employment emphasis under Federal contracts to be given to special disabled veterans and veterans of the Vietnam era. Directs the Secretary and the National Labor Relations Board to jointly develop procedures to determine whether a violation of a law listed above is serious enough to warrant debarment or suspension. Mandates a report by the Secretary and the National Labor Relations Board to the Congress on the implementation of this Act.