Detainee Basic Medical Care Act of 2008 - Directs: (1) the Secretary of Homeland Security to establish procedures for the delivery of medical and mental health care to all immigration detainees in Department of Homeland Security (DHS) custody; and (2) that such procedures address all detainee health needs, including primary care, emergency care, chronic care, prenatal care, dental care, eye care, mental health care, medical dietary needs, and other medically necessary specialized care.