Medicare Telemedicine and Medical Informatics Demonstration Act of 1997 - Directs the Secretary of Health and Human Services, through the Agency for Health Care Policy and Research, to make a grant to a consortium meeting specified criteria to provide for a project for the development and operation of telemedicine and medical informatics systems to demonstrate the application of high-capacity computing and advanced networks to the provision of health care to residents of medically underserved rural and inner-city areas. Requires the project to focus on Medicare beneficiaries and on improvements in primary care (and prevention of complications) for residents with diabetes. Lists project objectives, which include improving patient access to and compliance with appropriate care guidelines for chronic diseases through direct telecommunications link with information networks in order to improve patient quality-of-life and reduce overall health care costs. Authorizes appropriations.