Can anyone fill Janet Napolitano’s shoes?

It’s been two months since the Homeland Security secretary announced her plans to resign, but the White House still isn’t close to settling on a replacement, according to administration officials familiar with the search.

At least two potential candidates have rebuffed their advances. One of those is Michele Flournoy, a former deputy secretary of Defense who is deeply respected for both her policy and management skills. It’s unclear why Flournoy wasn't interested in the position (she was traveling and did not respond to a request for comment) but one possibility is that Flournoy, who was among those in the running this year to replace Leon Panetta as Defense secretary, would rather wait out the possibility of getting the top Pentagon job—either later in the Obama administration or in a future Democratic administration.

The sources did not reveal the name of the second potential candidate, apart from saying it was an individual who has experience running a large organization.

At the same time, two names that have repeatedly been mentioned in media reports as top candidates have not been in the running at all, according to administration officials. Thad Allen, a retired admiral and the ex-commandant of the Coast Guard, was assumed to be a likely candidate in part because of his widely praised response to Hurricane Katrina and the BP oil spill in 2010. Allen is also said to be a skilled manager and has considerable bipartisan support on Capitol Hill. But according to two administration officials, Allen has not been interviewed for the job.

Nor has John Pistole, the administrator of the Transportation Security Administration, a DHS sub-agency, who has quietly expressed interest in succeeding Napolitano, according to a senior administration official. Pistole also served as deputy FBI director until 2010.

Meanwhile, on Capitol Hill and among former DHS officials, the delay in filling in the role is beginning to provoke some anxiety.

It’s not unusual for cabinet departments to have high-level vacancies as the White House searches for replacements, but there tends to be more apprehension when these vacancies involve security-related positions. Since Napolitano's departure to become president of the University of California system, there have been numerous incidents that some say require the attention of a fully staffed Department of Homeland Security. Among them: the Navy Yard mass shooting, the terrorist attack in Kenya, and the continuing fallout from the Syria crisis.

"My worry is that it suggests the administration is doing a premature victory lap around al Qaeda, saying, in essence, ‘Who needs a secretary or even a deputy secretary? Al Qaeda is on the run and we can kick back,’” says Stewart Baker, who served as assistant secretary for policy from 2005 until 2009. "That's the impression you get with their lackadaisical approach to filling the job."

To be sure, the department’s acting secretary, Rand Beers, is a respected counterterrorism expert who has worked on the National Security staff of both Democratic and Republican administrations. White House officials also say that President Obama and his advisers are conducting a methodical search to find a candidate who has the range of experiences to take on one of the federal government's most daunting leadership challenges.

The department has only been without a confirmed secretary since early this month, when Napolitano officially stepped down. However, DHS has not had a permanent deputy secretary in place since the spring, when Jane Holl Lute resigned. Obama has tapped Alejandro Mayorkas, a top DHS immigration official, to be the deputy homeland security chief, but the nomination has stalled amid an investigation into whether Mayorkas used undue influence top help a politically connected technology firm with securing visas. (Mayorkas has unequivocally denied the allegations.)

"I'm flabbergasted that the administration has allowed these vacancies to pile up," says one former high-ranking DHS official, who declined to be identified criticizing officials he continues to work with. "It's one thing for it to take a while during the first years of an administration, but in year five they ought to have a well-oiled machine."

But administration defenders say the critics are neither being realistic about the challenges involved in finding confirmable candidates or about the real harm done by leaving positions open while a search is being conducted. "I know some think there are too many vacancies or people in acting positions, but the truth is, five years in, the folks who are there have substantial knowledge about the department's missions and the administration's priorities," says Sean Smith, a former DHS official and Napolitano spokesman. "It's a tough position to fill because of the breadth of the missions," adds Smith, noting that the department has law-enforcement, counterterrorism, immigration, cyber-security and disaster-relief responsibilities.

The apparent decision of Flournoy, in particular, points to another reality about the challenges of replacing Napolitano: Many potential candidates see little upside in the DHS job and much that could go wrong, potentially harming their professional trajectories. Homeland Security is a sprawling agency that handles a vast array of pressing security and policy issues, including counterterrorism, immigration enforcement and cyber-security and disaster-relief. The 240,000-employee department was cobbled together from 22 separate agencies in the wake of the 9/11 attacks and reports to no less than 100 different congressional committees and subcommittees. While DHS has perhaps outgrown infancy, it is a long way from being a fully mature federal agency that fits smoothly into the wider federal government.

"It's still in its terrible twos," is how one Obama administration official puts it.

Administration officials are looking for someone who has expertise in at least some of the department's missions, whether that is security, emergency management or disaster relief. But they are also looking for someone who has a proven record managing a large, complicated bureaucracy. And at the same time, entering their sixth year of an administration, the White House desperately wants someone who plays well with others. After a first term in which President Obama seemed proud to assemble a "team of rivals" cabinet, his aides now tout internal "chemistry" and a smoothly running "inter-agency" as one of their most important goals. That is especially important, they say, when Republicans in Congress remain so committed to blocking the president's agenda. "Our ships all have to be sailing in the same direction," says one White House official.

Many of the names that were floated soon after Napolitano announced her intention to step down, appear not to have gotten any traction. Among them is New York City Policy Commissioner Ray Kelly, who will be out of a job when Mayor Michael Bloomberg's term ends later this year. But Kelly carries baggage from what some view as overly aggressive police tactics, including his department's stop-and-frisk policy and its surveillance of Muslim communities. Nevertheless, both President Obama and Vice President Joe Biden have publicly touted Kelly in recent weeks. Still, in Washington such high-profile praise is often interpreted as a consolation prize when the job is really going to someone else.

But to whom? The White House apparently still doesn't know.