Veteran Medic Corpsmen Physician Assistant Demonstration Program Act of 2010 - Directs the Secretary of Veterans Affairs (VA) to establish a program to examine methods of enabling individuals with military medical or health professional work experience to build on such skills by entering into the physician assistant workforce. Outlines study requirements. Requires: (1) the Secretary to award grants to institutions of higher education with accredited physician assistant programs to carry out demonstration projects under the program; and (2) such institutions to give priority to individuals who serve or have served in the Armed Forces as a paramedic or other similar medical support position.