Federal Mask Mandate Limitations Act This bill requires prior congressional approval of any executive agency mandate that requires wearing masks or face coverings on commercial aircraft, trains, vessels, and public transportation. Before such a mandate may take effect, an agency must publish in the Federal Register and provide Congress and the Government Accountability Office (GAO) with scientific data, cost-benefit and economic impact analyses, and other information about the mandate's rationale. The GAO must, within 15 days, provide a report to Congress that assesses (1) the agency's compliance with the bill's provisions, and (2) the effect of the mask mandate on private-sector activity. Generally, the mandate shall not go into effect unless Congress approves it through a joint resolution; the bill sets procedures for the consideration of the joint resolution. However, the mandate may temporarily go into effect without congressional approval if the President determines the mandate is necessary to address (1) imminent health or safety threats or other emergencies, (2) the enforcement of criminal laws, or (3) national security.