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Washington Republicans disagreed Sunday on whether Eric Shinseki should be removed as the Department of Veterans Affairs secretary, following recent allegations about a secret waitlist for some patients, the most recent setback for the troubled agency.

Shinseki, who leads an agency still emerging from a backlog of veteran-patient claims, and other top agency officials were subpoenaed last week by the House Committee on Veterans’ Affairs, amid allegations that secret waiting lists were used to cover up long delays for doctors’ appointments and that some patients died waiting.

“He’s had five years to fix this,” Michigan GOP Rep. Mike Rogers said Sunday on CBS' “Face the Nation.” “If he can’t, we have to go in. The president is going to have to make a decision on Mr. Shinseki.”

The subpoenas also cover emails related to the purported list, compiled since early April at the Veterans Affairs medical center in Phoenix.

Former Defense Secretary Robert Gates said the problem is not Shinseki, a retired Army four-star general, it’s the agency.

“If there's one bureaucracy in Washington that's more intractable than the Department of Defense, it's V.A.,” Gates told CBS. “Give a lot of credit to Eric Shinseki. I think Secretary Shinseki has all the will in the world to do the right thing by veterans. He's totally committed. But he sits astride a very tough bureaucracy.”

Still, Gates and Rogers, chairman of the House Intelligence Committee, appeared to agree on two issues regarding the agency -- that the major problems appear to be below the secretary level and that Washington is giving the agency enough money to fix problems, including the backlogs and providing better mental-health care for veterans.

“I think, my own view is that the problem is below the secretary,” Gates said.

Said Rogers: “It just sure seems that they can't quite get it right at the mid-management level at the Veteran's Affairs."