Public Service Spending Integrity Act This bill restricts federal spending at businesses of the President, specified other officials, 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 certain authorized 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. A business shall be deemed to be owned or controlled by a covered individual or family member if any such person (1) is a member of the board of directors or similar governing body of the business, (2) directly or indirectly owns or controls more than 50% of the voting shares of the business, or (3) is the beneficiary of a trust which owns or controls more than 50% of the business and can direct distributions under the terms of the trust.