On the campaign trail, Donald J. Trump savaged the Department of Veterans Affairs, calling it a “disaster” and “the most corrupt agency in the United States.” He vowed to fire many workers at the department in an effort to fix a health care system fraught with delays.

As he transitions to the White House, he has tapped the agency’s harshest critics to advise him.

Mr. Trump has said he is considering Representative Jeff Miller, Republican of Florida, to run the agency. As the chairman of the House Committee on Veterans Affairs, Mr. Miller has hounded the agency for failing to enact meaningful changes to cut wait times and fire workers who hid delays. If selected, he will be the first secretary of veterans affairs who has never served in the military.

Mr. Trump’s transition team did not respond on Tuesday to a request for comment.

The team is being advised on policy by members of Concerned Veterans for America, a small conservative advocacy organization that is linked to the free-market activists Charles G. and David H. Koch and has long supported privatizing veterans’ health care.

For years, Concerned Veterans for America, based in Washington, was on the fringe of the veteran world, generally shunned by traditional veterans organizations.