Water Supply Permitting Coordination Act This bill makes the Bureau of Reclamation the lead agency for the purpose of coordinating all permitting and related activities required to construct certain new surface-water storage projects. Specifically, Reclamation must identify, notify, and coordinate all Federal agencies that may have jurisdiction over a review, analysis, opinion, statement, permit, license, approval, or decision for a qualifying project. A state where a project is being considered may also choose to participate as a cooperating agency. Reclamation's coordination responsibilities include (1) preparing a unified environmental review document, and (2) maintaining a consolidated administrative record and project data records. Additionally, Reclamation is authorized to accept and expend funds contributed by a nonfederal public entity to expedite the evaluation of a permit for such a project.