Bridgewater, New Jersey (CNN) As President Donald Trump, his arms crossed and his expression dour, warned North Korea on Tuesday of US "fire and fury," his new chief of staff sat across the table stone-faced.

John Kelly, sworn into his role a week ago Monday, once carried with him the hopes of a Washington establishment who believed his long career in the military could help apply rigor to both a quarrelsome West Wing and an erratic commander in chief.

On the first count, Kelly has seen initial success, according to half a dozen sources close to and within the White House. There are "fewer daggers" being lobbed internally, one source said.

Even close Trump confidants -- including family members like Jared Kushner and Ivanka Trump, and longtime aides like Hope Hicks and Keith Schiller -- have been subject to scrutiny from the new chief of staff.

But, as Trump's bombastic remarks on Tuesday demonstrated, there are few signs that his presence around Trump has tempered a mercurial and uncensored commander in chief.

Over the course of Kelly's first week in the White House, some viewed a milder Trump Twitter persona as an indication of his new chief of staff's sway. Kelly, according to a person familiar with his first week, spoke with Trump about his use of Twitter, which Trump has fiercely defended amid attempts by other confidants to moderate his voice.

A tweet-storm Monday ended hopes on the social media front, as Trump -- stuck indoors as rain pounded his golf course -- unleashed a string of tweets hammering the media, Democrats writ-large and, specifically, Sen. Richard Blumenthal, who had appeared earlier on CNN.

Speaking to Fox News this week, Kelly acknowledged that his advice would not always go heeded by the President he now serves.

"Remember, telling the unvarnished truth to power doesn't mean you always get your way," Kelly said in the interview, his first since assuming his position. "The principal ultimately decides and it is our way that so long as that decision is legal, moral and ethical, one salutes and executes."

"Sometimes you win," Kelly said, "and sometimes you don't."

Will Trump listen to the general?

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Tuesday's threat was a reminder Trump can change the course of the country with a few sentences in front of a camera.

"North Korea best not make any more threats to the United States," Trump said from a modified conference room in the clubhouse of Bedminster golf resort. "They will be met with fire and fury like the world has never seen. He has been very threatening beyond a normal state and as I said they will be met with fire and fury and frankly power the likes of which this world has never seen before."

Trump's bellicose statement was improvised in the moment, three people familiar with the situation said, though they reflected the same rhetoric that Trump has employed in private to discuss the rouge nation.

Kelly was "aware Trump would take a strong tone on North Korea," one official told CNN. He "certainly was not surprised or caught off guard," the official said.

Nonetheless, the moment alarmed establishment figures, Republican and Democrat alike. Sen. John McCain, the Republican chairman of the Senate Armed Service Committee, told Phoenix radio station KTAR that he prefers to see what Trump's national security team says, rather than the President.

"I don't pay much attention anymore to what the President says because there's no point in it," McCain said. "What I do pay attention to is what he does, and I can tell you that he has surrounded himself with an outstanding national security team. Gen. Kelly, (Defense Secretary James) Mattis, (National Security Adviser H.R.) McMaster. These are all really good people, and they're doing some of the right things."

McMaster and Mattis appealed to their fellow general to take the chief of staff job, according to people who know all three men. Both hoped Kelly could provide support to their national security advice, which Trump has at times discarded as overly similar to the approaches taken by the previous administration.

Former Defense Secretary Leon Panetta, who worked with Kelly during his tenure at the Pentagon, said he hoped Kelly will provide amplification to recommendations from the generals who comprise Trump's national security team.

"Kelly is not going to undercut others who are responsible for national security issues. It's just not what he does," Panetta said. "The relationship between Mattis, McMaster and Kelly should prove to add a lot of weight to what the national security team recommends to the President."

Sen. Al Franken, D-Minnesota, also urged Kelly to guide Trump.

"I would call on the new chief of staff, who I think is aware of the consequences -- the potential consequences of something like this -- I would call on him to tell the President not to do that kind of thing again," Franken told WCCO Tuesday.

Managing the staff or managing the President?

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People who have spoken with Kelly, both before he took the chief of staff role and after, say his top priority has remained bringing a fractious West Wing together.

Among his first steps has been to conduct interviews with White House staffers to glean information about their job and assess their effectiveness in advancing the President's agenda -- all with the goal of reorganizing the building to better serve Trump.

Kelly also delivered a speech to some 200 White House staffers last Friday in the large open foyer of the Eisenhower Executive Office Building in Washington.

Administration officials ranging from Kushner to lower ranking assistants heard a patriotic rallying call from Kelly, who warned that dividing the staff into establishment-versus-campaign operatives was damaging to Trump's goals.

Kelly has taken a stricter style in managing the flow of traffic in the Oval Office and aims to be present on most all policy-related calls. One of his top initiatives has been to cull the flow of information to the President, so Trump is largely receiving information critical to making a final decision on whatever matter is at hand, a source said.

Kelly traveled with Trump aboard Air Force One on Friday to Bedminster, and spent the weekend ensconced in the private club where Trump is spending the next two weeks. On Monday morning he updated the President on developments on the Korean peninsula, with Secretary of State Rex Tillerson piped in on the phone.

A President resistant to change

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But there are some Trumpisms that are unlikely to fade. He spitballs ideas with anyone within earshot, is prone to instantaneous decision making and prizes his ability to tweet straight to his base of supporters.

Kelly had hoped to moderate Trump's approach to the medium, according to a person familiar with the new chief of staff's approach. But he did not expect to completely reform a President who views his Twitter page as an unfiltered channel to the millions of supporters who thrust him into the White House.

Some Trump associates view Kelly's hands-off approach to Twitter with relief -- because it's not a battle he can win.

"I'm glad he doesn't try to take away the power of the President to tweet," a source said, in part because Kelly surely would've come up short and suffered a blow to his credibility early in his tenure.

Trump's longstanding habits have his friends questioning that he'll ever back away from the bombastic -- and sometimes seemingly erratic -- style that served him well in business and then later on the campaign trail.

In discussing Trump's fiery comments toward North Korea Tuesday, one source pointed out that Trump has a habit of using a "filter of billions" to speak to an audience of one, which could be the case with the President's barbed rhetoric toward Pyongyang.

"People who don't know him and don't understand that think it's harmful and scary," the source said.

But, the person added, "that's how he operates."