Public Service Spending Integrity Act This bill prohibits any federal funds from being obligated or expended for purposes of procuring goods or services at any business owned or controlled by a covered individual or any family member of such an individual. A "covered individual" is defined to include the President, the Vice President, the head of any executive department, and any individual occupying a position designated by the President as a cabinet-level position. The bill also prohibits the obligation or expenditure of funds from a Members' Representational Allowance or a Senators' Official Personnel and Office Expense Account for purposes of procuring goods or services at any business owned or controlled by the Member of Congress or any family member. No federal agency may enter into a contract with a business owned or controlled by a covered individual or family member. A business shall be deemed to be owned or controlled by a covered individual or family member, or by a Member of Congress or family member, if any such person: (1) is a member of the board of directors or similar governing body of the business, or (2) directly or indirectly owns or controls 51% or more of the voting shares of the business.