Washington (CNN) -- The White House has a big problem on its hands: finding someone to replace Defense Secretary Chuck Hagel, who was pushed out of the administration this week.
Since Michele Flournoy withdrew her name from consideration on Tuesday, there is a growing sense that many potential candidates may be shying away from the job due to the short time frame they would be in office and concerns over how independently they can function from the National Security Council, according to both current and former senior administration and congressional officials.
Flournoy cited family reasons for her decision to withdraw her name, but several administration officials say the decision came as a surprise because she had known she was on the short list of candidates being vetted. Another name now being widely circulated is former Deputy Defense Secretary Ashton Carter-who is widely credited with reforming cumbersome and expensive weapons acquisition procedures and programs, but who had clashed in the past with White House staff as well.
Pentagon: Hagel was not fired 
Pentagon: Resignation not about Iraq 
Obama announces Hagel's resignationThe scramble to find a new defense secretary comes as new details emerge over Hagel's departure from the administration. Hagel submitted his letter of resignation on Monday after it became apparent over a series of meetings with President Barack Obama that the president no longer wanted him in the job.
'Hagel didn't wait to be asked to leave,' a senior administration official close to Hagel tells CNN.
READ: Was Hagel doomed from the start?
Obama and Hagel had three conversations since late October, the last one being on Nov. 18.
'If you have three conversations with the President, you know where things stand', the official said.
After the final conversation, Hagel has a personal sense of 'inevitability' he would resign, rather than wait to be fired, the official said, describing to CNN in detail the secretary's actions and thinking.
The official said Hagel rapidly came to the conclusion after that final meeting he 'would not put up a fight,' to keep his job, but would instead resign 'giving the President options' to chart a different course. Hagel views his decision somewhat in military terms, when an officer submits his resignation knowing he will otherwise be fired.
The official said Hagel is 'at peace' with his resignation and believes it was the honorable thing to do.
'He knew he wasn't wanted,' the official said.
Hagel has been criticized for being a secretary who implements White House policy rather than being a dynamic member of a tight inner Obama circle offering new ideas and options. But this official strongly disputed portions of that characterization, saying 'even John Kerry isn't a member of that circle,' referring to the secretary of state.
READ: Chuck Hagel fast facts
While Hagel may not have regularly spoken up in large meetings, he did seek to be involved the official says. In September, he wrote a memo for Obama and the NSC to 'make the case' that the administration needed to look for more 'creative and active ways to deter Vladimir Putin,' the official said.
Behind the scenes, Hagel had grown deeply frustrated by the decision making process at the NSC, which is universally described as 'micromanagement.' Hagel joins former defense secretaries Leon Panetta and Robert Gates, who have also detailed NSC interference in both of their books and recent public appearances.
Hagel was also frustrated on several key issues where he had indeed offered specific views. He had wanted more immediate action on sending non lethal military aid to Ukraine, and also had written a memo calling for a clearer approach to US military and diplomatic action in Syria. The Pentagon was aware both memos had been poorly received at the National Security Council.
The official insisted that Hagel is fully supportive of the President's policy of not putting troops on the ground in Iraq in combat roles. If Obama pushed Hagel out because he is looking for a course correction on the war against ISIS in Iraq and Syria, it has not gotten to the point where Hagel or the chairman of the Joint Chiefs, General Martin Dempsey, have been asked for any new options.
OPINION: Pushing out Hagel not shake-up Obama needs
It now appears likely a confirmation hearing for Hagel's successor might not be scheduled before February, leaving a new Pentagon chief with less than two years on the job.
Several administration officials tell CNN the White House is also well aware any confirmation hearing could be a bruising fight given that Sen. John McCain (R-Ariz) is taking over the Armed Services Committee and is a deep odds with the White House over Syria and Iraq.
That all adds up to a relatively short term in office likely that will almost certainly be characterized by fights with a Republican Congress on everything from the war against ISIS to potential mandatory spending cuts.
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