Public and Teaching Hospital Preservation Act - Amends the U.S. Troop Readiness, Veterans' Care, Katrina Recovery, and Iraq Accountability Appropriations Act of 2007 to extend by one year the moratorium on: (1) implementation of a rule relating to the federal-state financial partnership under titles XIX (Medicaid) and XXI (State Children's Health Insurance Program) (SCHIP) of the Social Security Act; and (2) finalization of a Medicaid rule regarding the treatment of graduate medical education (GME).