High-profile vacancies atop the Department of Homeland Security and the Department of Health and Human Services have left White House officials searching for candidates to fill two of the Cabinet posts most closely associated with President Trump's agenda.

Despite the importance of healthcare and immigration policies to Trump, who championed overhauls to both on the campaign trail, the White House has not yet settled on leading contenders for either open post. DHS has weathered a trio of devastating hurricanes and the initiation of a legislative debate about immigration reform with a temporary leader at its helm for more than two months.

Elaine Duke, acting DHS head, has presided over the agency since Trump elevated his original DHS secretary, John Kelly, to White House chief of staff in late July.

The resignation of HHS Secretary Tom Price last week capped off months of healthcare failures on Capitol Hill, where Trump's team had once hoped Price would wield influence due to his years of experience as a congressman from Georgia. Trump was frustrated by the collapse of Obamacare repeal efforts, but ultimately dismissed his HHS secretary over the unrelated controversy surrounding Price's private jet use.

A senior White House official told the Washington Examiner that the search for a DHS nominee is further along than the search for Price's replacement simply because the DHS selection process started months before the process presently underway at HHS.

That official said Kelly has been hands-on when it comes to choosing his successor at DHS, where his performance on border security in particular caught the president's eye and landed him his position in the West Wing.

White House aides are still examining a number of contenders for both Cabinet positions.

Seema Verma, administrator of the Centers for Medicare and Medicaid Services, emerged as an early potential candidate at HHS, as did Veterans Affairs Secretary David Shulkin, a physician.

Shulkin's own travel controversy has invited an inspector general investigation and likely sidelined him in the race for HHS secretary, however. At least one health industry executive has also been floated as a contender by people close to the White House.

At DHS, the two-month head start officials had to find a new secretary does not seem to have produced any more certainty as to who will receive the nomination than at HHS.

Duke is considered a candidate to take over the top job on a permanent basis.

But the White House has moved slowly to whittle down the list of other names, and has demonstrated little urgency in filling the position as officials pump a steady stream of lower-level appointments into Senate committees.

Keith Appell, a GOP public relations operative who served as the so-called "sherpa" responsible for guiding Attorney General Jeff Sessions through his confirmation earlier this year, said the administration will seek out candidates whose views on healthcare and immigration align with Trump's populist agenda despite the potential obstacles those nominees may face in the Senate.

"I think that regardless of the current circumstances, whenever there's a new Republican administration — I imagine it's the same with the Democrats — there are certain agencies that the base supporters look at through the prism of ‘personnel is policy,' and that usually includes the attorney general, health and human services, even education, maybe a couple of others," Appell told the Washington Examiner.

"Whereas defense, state, homeland security ... people can still accommodate someone who's less ideological because of the range of issues that those departments deal with, with the possible exception of the issue of immigration in the Department of Homeland Security, because that is such a big part of the Republican agenda in terms of the Trump agenda," Appell added.

Indeed, Trump's picks for the Departments of Defense and State both came from outside the world of partisan politics. Defense Secretary Jim Mattis required a waiver from Congress to take the reins at the Pentagon earlier this year due to the proximity of his appointment to his military service, and Secretary of State Rex Tillerson had no political experience prior to his transition from the CEO of Exxon Mobil to the nation's chief diplomat.

Appell said he could envision the White House selecting someone who is less conservative to lead Homeland Security so long as that person shared Trump's views on immigration.

"At HHS, that's a department where both parties prefer to have a leader who is fully in line with the president's agenda," he said. "I think that the president is also going to look for a nominee who is in line with the social issue agenda the way Tom Price was."

Amid the hunt for two new Cabinet secretaries, one of the most high-profile ones infuriated the president this week when NBC News published a report that suggested he had called Trump a "moron" and threatened to resign.

Tillerson confronted reporters on Wednesday to deny that he ever discussed a departure from the administration with Vice President Mike Pence or other officials during a turbulent period over the summer.

But the damage was done with West Wing aides, who privately fumed over the headlines Tillerson had created, according to a source close to the White House.

"The Trump people are very unhappy with Tillerson," the source told the Washington Examiner. "You don't air your dirty laundry to other administration officials like that."

"That's something that, as a former global CEO, he knows what's appropriate and not. I think the job's starting to get to him a little bit, or the frustrations are," the source added. "It's understandable why Tillerson has frustrations ... [Trump's] use of Twitter in foreign policy is a new thing."

Despite the tensions between Tillerson, the president and other Cabinet officials, the secretary of state has said he has no plans to resign, and other White House aides have said Trump has no plans to ask for his resignation.