Affordable Care Accountability Act of 2013 - Amends the Patient Protection and Affordable Care Act (PPACA) to require any employer contribution made on behalf of the President, Vice President, or any political appointee to be paid only to the issuer of a plan through an American Health Benefit Exchange (a state health insurance exchange created under PPACA), and not through the federal employees health benefit program. (Currently, this requirement applies to Members of Congress and congressional staff.)