Manufacturing Economic Recovery Act of 2013 - Amends the Internal Revenue Code to allow: (1) a manufacturing recovery tax credit for investment in manufacturing real and tangible personal property used in the United States, including an increased credit for manufacturing property located in an economically disadvantaged area and an extremely economically disadvantaged area; (2) an additional investment tax credit for manufacturing property; and (3) a work opportunity tax credit for hiring an employee in a manufacturing facility located in the United States (manufacturing recovery employee), including an increased credit for hiring individuals receiving unemployment compensation.