The enthusiasm was understandable at one level: Mr. Price has been a member of the A.M.A. house of delegates since 2005 and was an alternate delegate for a decade before that, according to the A.M.A. and the Medical Association of Georgia.

“For those who are attacking Dr. Price, I have to ask whom you would rather have at the helm of H.H.S. — a career bureaucrat? A former governor who views doctors as a cost center to be controlled?” said Dr. Robert E. Hertzka of San Diego, an anesthesiologist and former president of the California Medical Association. “Tom Price may turn out to be the best friend that physicians and patients have ever had in that role.”

Many doctors are not willing to take that chance. More than 750 people who identify themselves as members of the A.M.A. signed a letter to the association’s board objecting to the endorsement.

The “unqualified support” for Mr. Price is inappropriate, the letter says, because he has been “a strong opponent of so much of our clearly delineated A.M.A. policy” on issues like the Affordable Care Act, contraception and gay rights. Some doctors also said patients could be hurt by major changes in Medicare and Medicaid that Mr. Price, along with other House Republicans, has advocated.

Dr. Andrea S. Christopher, 32, an internal medicine doctor at the veterans hospital in Boise, Idaho, said she had decided not to renew her A.M.A. membership over the endorsement, which she called especially upsetting to her generation of physicians. “Dr. Price has been an outspoken opponent of the Affordable Care Act, which has done so much to address the needs of our most vulnerable patients and reduced the uninsured rate to the lowest level on record,” Dr. Christopher said.

Dr. Kristin M. Huntoon, a 37-year-old neurosurgery resident at Ohio State University in Columbus, said the group’s support for Mr. Price had increased the chances that the Affordable Care Act would be dismantled — and that has put her patients at risk.

Ohio has extended Medicaid coverage to more than 600,000 people under the federal health care law. If that expansion is reversed, Dr. Huntoon said, some patients will not receive imaging or treatment at an early stage of their disease, and they are more likely to arrive when tumors have spread to the brain. “At that stage,” she said, “there’s often nothing I can do for the patient.”