Prioritize Spending Act of 2013 - Requires amounts necessary for incurred federal obligations, in the event that the public debt reaches the statutory limit, to be made available to certain obligations, in prioritized order, before all other obligations.

Prioritizes such obligations in the following descending order: (1) amounts necessary to carry out the authority of the Department of the Treasury to pay with legal tender the principal and interest on public debt; (2) amounts determined by the Secretary of Defense (DOD) (and the Secretary of Homeland Security [DHS] in the case of the Coast Guard) to be necessary to continue to provide pay and allowances (without interruption) to members of the Army, Navy, Air Force, Marine Corps, and Coast Guard, including their reserve components, who perform active service; (3) amounts certified to Congress by the President as necessary to carry out vital national security priorities; (4) amounts necessary to carry out the authority of the Commissioner of Social Security to pay monthly old-age, survivors', and disability insurance benefits under title II of the Social Security Act (SSA); and (5) amounts necessary to make payments under the Medicare program under SSA title XVIII.