National Statuary Hall Collection Progress Assurance Act This bill establishes a timeline for the Joint Committee on the Library to approve or disapprove requests for replacing statutes (or any related actions that are subject to Joint Committee approval) in the National Statutory Hall of the U.S. Capitol. The Joint Committee oversees operations of the Library of Congress, as well as management of the National Statuary Hall, the U.S. Botanic Garden, and works of fine art in the Capitol. Generally, the bill requires the Joint Committee to approve or disapprove a request to replace a statue not later than 30 days after the Architect of the Capitol forwards the request to the Joint Committee. If the Architect forwards the request before the Joint Committee's first organizational meeting of a Congress, the Joint Committee must approve or disapprove the request not later than 30 days after the Architect forwards the request to the Joint Committee or the date of the meeting, whichever is later.