January 8th National Memorial Act This bill directs the Department of the Interior to establish the January 8th National Memorial in Tucson, Arizona, as an affiliated area of the National Park System in commemoration of the shooting of Congresswoman Gabrielle Giffords and 18 others in Tucson on January 8, 2011. The January 8th Memorial Foundation shall transfer to Pima County, Arizona, amounts equal to final funding pledges, in addition to the amounts that the foundation has raised and transferred to the county for the construction of the memorial. The memorial shall be constructed on property owned by Pima County. The bill makes the county responsible for the management of the construction contract for the memorial through the use of funds provided by the foundation. The foundation shall cease operations after (1) final funding pledge amounts have been paid to Pima County, and (2) construction of the memorial has been completed. Pima County shall (1) be the memorial's management entity, and (2) be responsible for the construction and operation of the memorial. Interior shall develop a general management plan for the memorial.