Who will be the next head of the VA?

It could be the most high profile job opening in the country at the moment: secretary of Veterans Affairs.

The White House will not put a timetable on Secretary Eric Shinseki's replacement, but it is looking for someone, it says, with experience managing big systems.

President Obama's search for a permanent Veterans Affairs secretary will have to answer one key question: Does military service have to be on the resume?

Since the department's creation, there has been an unbroken line of veterans serving at the top.

But the VA is the nation's largest health care system, scheduling 85 million appointments a year.

And like a troubled business, it may need a turnaround expert.

John Hudak studies bureaucracy at the Brookings Institution.

"The reality is you need someone who is familiar with bureaucratic management as well as military issues, and that individual is often hard to find," he said.

With Shinseki's ouster, his deputy, Sloan Gibson, a West Point graduate, is now temporarily in charge.

But the president may consider more high profile names to fill the role.

People inside and outside the government are already speculating on several:

General Ray Odierno, who led U.S. forces in Iraq and is now Army chief of staff. He once bluntly said military efforts to eliminate sexual assault in the ranks were "failing." He could bring candor to the job.

Mike Mullen, former chairman of the Joint Chiefs of Staff for Obama and George W. Bush. He could appeal to both parties.

And Rep. Tammy Duckworth of Illinois, who lost both of her legs in Iraq. She would bring experience, having already served as an assistant secretary in the VA.

Tom Tarantino with the Iraq and Afghanistan Veterans of America wants bold action.

"We have to look towards the future," he said. "The VA is an organization that is terminally stuck in the mid-20th century. And they have squeaked through over the last few years to try to modernize, but it's not enough."

The greatest challenge for the next head of the VA may be finding a way to bridge the differences over the best way forward. Some Republicans want to move toward privatizing parts of the VA while some Democrats say the current system needs more investment.