Federal Permitting Modernization Act of 2023 This bill revises environmental review requirements for certain infrastructure projects under the National Environmental Policy Act of 1969 (NEPA) and the Fixing America's Surface Transportation Act. Specifically, this bill establishes deadlines for federal agencies to complete the environmental review of such projects. In addition, the bill limits when a court may provide injunctive relief in a case about the environmental review or authorization of an infrastructure project. A court may not issue a temporary restraining order or preliminary injunction against an agency or a project sponsor in connection with the review or authorization of an infrastructure project unless the court determines that (1) the environmental review has failed substantially and materially to comply with the requirements of NEPA, and (2) the failure cannot be cured by supplementing the environmental document or other mitigation and monitoring measures.