Federal Hiring Freeze Act of 2013 - Prohibits the head of an executive agency from appointing an individual to any position in such agency during a fiscal year for which the Director of the Office of Management and Budget (OMB) projects that there will be a federal budget deficit. Authorizes the President to waive such prohibition under specified circumstances, including the existence of a state of war or other vital national security concern or the need to make appointments to law enforcement positions, the United States Postal Service (USPS), or the Federal Aviation Administration (FAA).