Veterans Health Care Access Received Closer to Home Act of 2014 - Expresses the sense of Congress in support of veteran-centric health care coordination between the Department of Veterans Affairs (VA) and community providers, as well as cost-effective VA purchase of veterans' care from the private sector.

Amends the Veterans' Mental Health and Other Care Improvements Act of 2008 to reauthorize a VA pilot program of contract care authority within specified Veterans Integrated Service Networks for the health care needs of veterans in highly rural areas. Requires: (1) that medical appointments for veterans, under the pilot program, occur during the 30-day period beginning on the date that is 15 days after the appointment is requested, and (2) the Secretary of Veterans Affairs to ensure that eligible veterans are informed of the program.