Back to Work Tax Credit - Amends the Internal Revenue Code to allow an increased work opportunity tax credit for the hiring of a qualified long-term unemployed individual. Defines "qualified long-term unemployed individual" as any individual who was not a student for at least six months during the one-year period ending on the hiring date and is certified as having aggregate periods of unemployment during the one-year period ending on the hiring date which equal or exceed six months. Allows tax-exempt charitable organizations or public institutions of higher education to claim the lesser of the amount of the work opportunity credit or the amount of payroll taxes paid during the calendar year for hiring qualified long-term unemployed individuals.