Unfortunately, the AMA has name recognition among the general public. Until the majority of docs who do not support the AMA form their own publicly identifiable group, the public will feel they need to follow the AMA’s “advice”.
There already is such an organization, one that has opposed socialized medicine consistently in all its various incarnations since 1943. It's name is the Association of American Pysicians and Surgeons (or AAPS) and its membership includes some current members of Congress.
http://www.aapsonline.org