Veterans Affairs Health Workforce Enhancement Act of 2014 - Directs the Secretary of Veterans Affairs (VA) to establish medical residency programs, or ensure a sufficient number of residency positions in medical residency programs, at any VA medical facility that the Secretary determines is experiencing a shortage of physicians.

Requires the Secretary to determine the specialty of health care professionals that each such facility is experiencing a shortage of and allocate residency programs and positions based on such determination.

Directs the Secretary, during the five-year period beginning on the enactment of this Act, to increase the number of graduate medical education residency positions at VA medical facilities by not less than 2,000 positions, giving priority to medical facilities that: (1) do not have a medical residency program, and (2) are located in a community in which there is a high need for health care for veterans.