Public Health and Medical Emergency Coordination Act of 2006 - Amends the Public Health Service Act to transfer the functions, personnel, assets, and liabilities of the National Disaster Medical System to the Department of Health and Human Services (HHS). (Currently, such System is directed by the Secretary of Homeland Security.) Designates HHS as the primary agency for the coordination of federal assistance to supplement state, local, and tribal resources for preparing for or responding to a bioterrorist attack or other public health or medical emergency.