Dr. McCance-Katz began her career at Yale, later moving to the Albert Einstein College of Medicine and the University of California, San Francisco, building an expertise in treating drug addiction with medications. She was medical director of California’s Department of Alcohol and Drug Programs, before becoming the first chief medical officer at the Substance Abuse and Mental Health Services Administration, or Samhsa, the primary federal agency overseeing substance abuse and mental health services, in 2013. The medical officer serves under the agency’s director.

The person most responsible for creating the czar position, Representative Tim Murphy, Republican of Pennsylvania, a practicing psychologist, also objects to Dr. McCance-Katz’s nomination, but for another reason. Mr. Murphy, as chairman of a congressional subcommittee, investigated federal mental health programs after a 20-year-old man with severe mental illness shot and killed 26 elementary school students and teachers at Sandy Hook school in Newtown, Conn., in 2012. He found fault with Samhsa for not sufficiently addressing the hardest-to-treat forms of mental illness, and for using some of its funds to support organizations and conferences where participants encouraged patients to go off their physician-prescribed psychiatric medicines.

Mr. Murphy said he was disturbed that Dr. McCance-Katz publicly defended the agency as efficient and effective during her two-year tenure as the leading physician at Samhsa. “She does not have my confidence,” Mr. Murphy said in an interview. “When she was there, she knew there was a problem, and she didn’t speak up,” he said. “We never heard from her.”

Samhsa, where Dr. McCance-Katz served as chief medical officer from 2013 to 2015, has itself become a lightning rod in the debate. In fact, Dr. McCance-Katz has sent mixed signals about her preferences. She defended the agency while there, but after leaving she wrote a sharp critique in Psychiatric Times concluding that its approach “includes a focus on activities that don’t directly assist those who have serious mental illness.”

Mr. Murphy and members of his staff said he had raised his concerns about the nominee directly with the secretary of health and human services, Dr. Tom Price, and Vice President Mike Pence.

Representative Murphy has also attacked the choice publicly, on Twitter and in interviews. Many people following the drama, both inside and outside Washington, believe that he is upset that the White House passed over his favored candidate. According to Mr. Murphy’s staff, that was Dr. Michael Welner, a prominent and controversial New York forensic psychiatrist who helped develop the legislation that created the position.

In an email, Dr. Welner confirmed that Mr. Murphy had approached him about recommending him to the Trump administration for the position. He said he initially declined, because of the sacrifices involved, but later accepted because of the prospect of saving lives. He said he believed that federal mental health funding should be refocused on the most costly mental health challenges and on evidence-based treatments.