Public Service Spending Integrity Act This bill restricts federal spending at businesses of the President, specified other officials, Members of Congress, or their family members. Specifically, the bill prohibits 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 family member of such individual, except for security purposes. 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. No federal agency may enter into a contract with a business owned or controlled by a covered individual or family member. The bill also prohibits the obligation or expenditure of funds from a Member's Representational Allowance or a Senator's 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, except for security purposes. 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.