No Taxpayer Funding for the Wall Act This bill prohibits the use of federal funds to construct physical barriers or related infrastructure along the southern U.S. border by federal departments or states that receive federal funding. The President is authorized to enter into a treaty where a foreign country agrees to pay for constructing such a physical barrier. The Government Accountability Office (GAO) shall conduct yearly audits of federal departments and states that receive federal funding to ensure compliance with this prohibition. The bill authorizes penalties against departments or states when the GAO is unable to confirm compliance. The bill directs the Office of Management and Budget (OMB) to report the budgetary impact of any executive order or presidential memorandum related to border security issued from FY2019 to FY2023. OMB shall also establish a public website tracking non-federal funds, including those received from foreign governments, for building physical barriers along the southern U.S. border.