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The Defense Secretary job opening is emerging as a thanks-but-no-thanks opportunity, as some of the top potential prospects have already said they’re not interested in the job.

Within minutes of reports Monday that Secretary Chuck Hagel would resign, the names of Michele Flournoy and Rhode Island Sen. Jack Reed emerged as top prospects.

But each made clear by the end of the day that they didn’t want the coveted but high-wire, Cabinet-level post.

The new secretary would indeed step into a difficult and complicated world, with the emergence of the deadly and unpredictable militant group Islamic State, amid Defense Department cuts.

“There’s no question a lot is going on around the world and at the Pentagon,” department spokesman Rear Adm. John Kirby told Fox News on Tuesday.

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    In addition, there have already been three defense secretaries in Obama’s first six years. And with his administration ending in 2016, the incoming secretary isn’t assured much job security.

    Kirby argued that Hagel’s departure after two years was not “abnormal.”

    To be sure, his two predecessors -- Robert Gates and Leon Panetta -- stayed about the same amount of time, which is not unusual in the high-pressured White House environment.

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    Whether Hagel resigned or was forced out by Obama might never be known. However, what appears clear is he and Obama didn’t have a shared vision for the next two years.

    “I think both men determined that this was the right time for [Hagel] to step down,” Kirby said. “Now he believes, and president agrees, it’s time for a new leader to take the ranks.”

    Michael O’Hanlon, a foreign policy expert at the Brookings Institution, says he “mostly” disagrees with the argument that Obama will have trouble filling the job.

    “I think most Americans who have the preparation and were asked would say yes,” O'Hanlon said Wednesday. “And I’m talking about those who meet a high standard.”

    He also argues that the next Defense secretary should be on better footing, considering Obama appeared to replace Hagel amid pressure for a shakeup after Democrats’ big midterms losses.

    Obama won’t have the same political cover for another quick exit, O'Hanlon argues. He thinks such a situation would further highlight that the president is the “architect” of Middle East military policy, including the limited presence in Syria against Islamic State to which some top military leaders seem opposed.

    “He needs to be willing to show some flexibility,” O'Hanlon said.

    Reed, a Democrat, stepped aside Monday afternoon through his statement from his Capitol Hill Office, which stated, in part, that he “loves his job and wants to continue serving the people of Rhode Island.”

    Flournoy, chief executive for the think tank Center for a New American Security and a former undersecretary of Defense for Policy, cited family concerns in withdrawing from possible consideration.

    However, Flournoy’s decision has sparked speculation about her or other potential candidates not wanting to join the Obama administration, which faces intense criticism of its handling of crises in the Middle East and elsewhere in the world.

    Political observers also point out they might instead be waiting and hoping that Hillary Clinton or any other Democrat wins the White House in 2016.

    Kirby disagrees with speculation that morale is low at the Pentagon.

    “It’s high,” he said. “We’re mission focused.”

    Other candidates reportedly being considered include Ashton Carter, the deputy defense secretary from October 2011 to December 2013, and Homeland Security secretary Jeh Johnson. Robert Work, who currently holds the No. 2 job at the Pentagon, is also seen as a possible contender.

    Johnson previously served as the Pentagon's general counsel and is highly regarded by the West Wing, particularly following the month-long process he oversaw to identify the immigration executive actions Obama announced last week.

    But given Republicans' staunch opposition to that action, tapping Johnson for the Pentagon poses the risk of turning his confirmation hearing into a fierce debate on immigration. The president also would need to fill the top job at Homeland Security again just as the department is implementing the immigration actions.

    The White House has no comment on the process to nominate Hagel's successor.

    "The president is considering a number of well-qualified candidates; however, I don't have any personnel announcements at this time," National Security Council spokeswoman Bernadette Meehan said Tuesday.

    The Associated Press contributed to this report.