Greening the Healthcare Workforce Act of 2008 - Directs the Administrator of the Environmental Protection Agency (EPA) to provide grants to nonprofit hospitals or health care institutions to promote environmentally sustainable practices in building and maintenance operations, including: (1) the training of employees in environmentally sound waste management and chemical management practices; (2) the reduction in use of mercury-containing medical supplies; and (3) the conduct of minor improvements to grounds and facilities to improve energy efficiency and indoor air quality and to reduce water waste.