WASHINGTON — Rex Tillerson wants Americans to sleep well at night, even with a trigger-happy dictator in North Korea and a Twitter-tapping president at the White House threatening nuclear Armageddon.

But Tillerson's task as the nation's chief diplomat facing his first major international crisis is tougher than promoting sweet dreams. He must try to tamp down President Trump's threat of "fire and fury" with an oilman's background, a depleted senior staff, a threatened budget crunch and a power struggle with the White House.

Whether the secretary of State is up to the job — or whether he may even be contemplating a hasty exit, or "Rexit," from Foggy Bottom — is one of the central questions facing Washington's foreign policy cognoscenti as Tillerson completes his trek through southeast Asia.

"Don't quit yet!" was the plea last month from Aaron David Miller, a former State Department diplomat in Republican and Democratic administrations. Now a vice president at the Woodrow Wilson International Center for Scholars, Miller says the White House needs to give Tillerson the flexibility to do his job.

"Trump hasn’t empowered him" over other administration officials, such as United Nations Ambassador Nikki Haley and White House adviser and Trump son-in-law Jared Kushner, Miller said. The president, he said, "has to literally restrain his own instincts when it comes to doing foreign policy on Twitter and let Tillerson be perceived as the repository of authority.”

That didn't happen this week, when Tillerson was seeking to enforce economic sanctions that could lure North Korea to the bargaining table while Trump was threatening "fire and fury like the world has never seen." Rather than part of a coordinated strategy, Trump's words were improvised on the spot, The New York Times reported. Trump on Friday offered a fresh threat of force against North Korea, writing on Twitter that “military solutions are now fully in place, locked and loaded,” if Kim's regime should “act unwisely.”

Nor did it happen last month, when Tillerson sought to mediate between Qatar and four Persian Gulf neighbors led by Saudi Arabia, even as Trump took the neighbors' side and called Qatar "a funder of terrorism at a very high level."

Tillerson alluded to the cacophony at the time, telling reporters his new job "is a lot different than being CEO of Exxon, because I was the ultimate decision-maker. That always makes life easier."

Because any military solution to the North Korean nuclear buildup would be catastrophic in terms of loss of life, sanctions and diplomacy represent nearly everyone's first choice. But while seeking to beef up the Pentagon, Trump has proposed a 30% cut at the State Department.

“The problem is that this administration, this president and even this secretary of State have downsized their commitment to the State Department,” said Rep. Eliot Engel, ranking Democrat on the House Foreign Affairs Committee. “It just goes to show what happens when you don’t do diplomacy before you do everything else.”

Now Tillerson faces several problems navigating Washington, much less North Korea:

• As has been the case in past administrations, the State Department is but one foreign policy power center. It competes with the Pentagon, National Security Council and others for the president's attention. Under Trump, the problem is "multi-polar," Miller said.

"I've never, ever seen anything like this," he said. "Tillerson needs to be in sync with the president, in word and in deed."

• The administration has been slower than its predecessors in filling senior jobs, and the State Department has been among the slowest, in part because of disputes with the White House.

Only 24 of 131 jobs requiring Senate confirmation have been filled; most of those are ambassadors to individual countries. There still is no undersecretary for arms control, assistant secretary for East Asian and Pacific affairs, or ambassador to South Korea.

"There just has not been sufficient prioritization in terms of filling these jobs," said Max Stier, president of the Partnership for Public Service. He said Tillerson's effort to reorganize the department and cut the budget by 28%, as Trump has proposed, was like trying to "re-engineer the airplane while you're flying it."

• Tillerson himself, chosen after Trump discarded more experienced prospects such as former Republican presidential nominee Mitt Romney and former Central Intelligence Agency director David Petraeus, came with no government experience from his job at Exxon Mobil.

Yet the State Department pushed back Wednesday against the argument that the administration's North Korea strategy and rhetoric were discordant. Spokeswoman Heather Nauert said the White House, State Department and Pentagon are "on the same page" and "speaking with one voice."

That echoed remarks by Tillerson himself during a refueling stop in Guam — the U.S. territory that North Korea, ironically, threatened to strike even as the secretary was heading there.

"We have a very active, ongoing diplomatic effort, most of which is behind the scenes, because that’s where diplomacy is most effective," he said. At the same time, he added, Trump "felt it necessary to issue a very strong statement directly to North Korea."

Tillerson said U.S. seeks dialogue with North Korea if it abandons nuclear program

Analysis: Why the latest sanctions on North Korea may fail