The questions surrounding the VA's leadership come amid growing controversy about the department's handling and oversight of hospitals dedicated to caring for the nation's veterans. Various congressional and government investigations of the agency have been conducted. The results of those investigations have suggested lapses in operational control at some facilities and problems with communication and oversight within the agency. (CNBC conducted its own investigation as well).
Multiple sources, including Rep. Jeff Miller, R-Fla., chairman of the House Committee on Veterans' Affairs, told CNBC they believe lower-level bureaucrats within the department are keeping certain damning reports from the secretary.
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"Unfortunately, part of the problem is there is a midlevel bureaucracy within VA that will not give the secretary the information that he needs to do his job," Miller told CNBC in an interview in November.
"It's a system management problem," he said.
Take the response one whistle blower, who worked with the U.S. Office of Special Counsel on two investigations of the VA, got from a director at the agency's headquarters when queried about whether Shinseki had been informed about patient care issues.
"He told me 'we don't bother him (Shinseki) with these things; we only tell him the good news'," the source told CNBC on the condition of anonymity.
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That source worked for eight years at the Jackson VA in Mississippi and the VA in Gainesville, Florida, the largest in the country.
But problems with the agency's hospital oversight have weighed on the department's leadership. So much so that some—VA headquarters sources, former VA employees and congressional sources who spoke to CNBC anonymously for fear of their jobs—believe Shinseki tried to tender his resignation at least once last year, but was rebuffed by President Obama.
CNBC was unable to confirm those claims, and the White House declined to give any comment.