Washington (CNN) Administration aides have grown increasingly skeptical the summit between President Donald Trump and North Korean leader Kim Jong Un will come to fruition amid harsh rhetoric from Pyongyang and concerns over the meeting's agenda, officials and other people familiar with the matter said.

Even as teams of advance staffers survey ornate hotel ballrooms in Singapore for the June 12 encounter, some of the President's advisers privately say the chances of the talks occurring grew slimmer after North Korea adopted a harsher tone toward the US last week and raised questions about Kim's commitment to, and definition of, denuclearization.

Trump himself remains committed to meeting Kim, and there has not been any indication he is preparing to call off the meeting himself, the officials said. But the new developments have led to a renewed impression that the audacious diplomatic meeting may not be as likely to occur as it once seemed.

Trump administration officials have also grown concerned that the President is overly eager for the summit to take place, increasing Kim's leverage should the talks take place, US officials and a source close to the administration said.

"I don't think the President gets cold feet about anything," said Treasury Secretary Steve Mnuchin when asked Monday by reporters at the White House whether Trump was reconsidering his participation in the summit. "The President is set. Right now it's still on. If that changes, you'll find out about it."

But Vice President Mike Pence made clear Trump might change his mind. "It would be a great mistake for Kim Jong Un to think he could play Donald Trump," Pence told Fox News on Monday. Asked whether Trump was willing to abandon the summit if his terms aren't met, Pence said "there's no question."

Moon meeting key

The recent pangs of anxiety will come to a head on Tuesday when Trump meets in the Oval Office with South Korean President Moon Jae-in, who some US officials believe oversold North Korea's willingness to negotiate away its nuclear program. In March, Moon's envoy told reporters in the White House driveway that Kim is "committed to denuclearization" and understood that joint US-South Korea military exercises "must continue."

But statements last week from North Korea indicated otherwise. The North threatened to withdraw from the Trump talks if the joint exercises proceeded or if the US continued to insist Pyongyang abandon its nuclear program.

Moon, who also spoke to the President by phone on Saturday, hopes to keep the summit on track, believing the recent diplomatic warming has forestalled the possibility of US strikes on North Korea.

"Probably more than anyone else -- more than Trump, more than Kim Jong Un -- there is more at stake for Moon Jae-in than either of them," said Joseph Yun,the former US special representative for North Korea policy. "And so he will be desperate to make sure that there is a meeting. And I would expect he will make his best pitch."

Now, Moon will need to convince Trump to stay the course, reassuring him the direct talks with North Korea can still be the success he once promised Trump they would be.

"President Moon has to really deliver in terms of making President Trump feel like this summit isn't going to go bust," said Sue Mi Terry, a former CIA analyst and Korea expert. "No one wants to walk into a meeting that's going to fail. I think tomorrow's meeting is critical in terms of whether we're really going to have Washington and Pyongyang meeting."

Terry, who met last week with South Korean officials, said she believes Moon will make the case that Kim was simply trying to "save face" with the threats and tough statements issued last week, but not pulling back from a willingness to denuclearize.

"I think President Moon is going to try to explain North Korea's position," Terry said. "Moon will try and do a lot of talking on Kim's behalf. And if President Trump is not convinced, then there's no meeting."

If the summit is scrapped, the only alternative the President and his allies have floated is military action.

Late last week, Trump warned North Korea it could go the way of Libya and Iraq and be "decimated" if it refuses to strike a deal. The President's allies parroted those warnings in recent days.

"President Trump told me three days ago that he wants to end this in a win-win way. He thinks that's possible, but if they pull out, they play him, that we're going to end North Korea's threat to the American homeland in his first term and I'll let you surmise as to what that might look like," said Sen. Lindsey Graham, an outspoken North Korea hawk, on "Fox News Sunday."

Yun, who is now a CNN global affairs analyst, said he believes Trump remains committed to the summit and "is not going to be the one to pull the plug."

Beyond ensuring Trump remains committed to the summit, Yun said Moon would do well to also provide "a dose of reality" about what it will take for North Korea to agree to denuclearize.

The Trump administration's maximalist position on denuclearization -- refusing any sanctions relief until North Korea denuclearizes -- has irked North Korea, which is advocating for a phased approach to denuclearization and sanctions relief.

Intensive negotiations

Trump's meeting with Moon on Tuesday follows a week of intensive discussions between American and South Korean officials attempting to decipher the North's harsher tone. John Bolton, the President's national security adviser, spoke to his South Korean counterpart several times after gaining little clarity during an initial call on Wednesday.

Inside the West Wing, where the statements came as a surprise, aides have become more pessimistic about Kim's intentions after weeks of positive signs, including the release of three Americans being held prisoner in North Korea. Some national security aides are worried that with just three weeks remaining before the summit there isn't enough enough time to coordinate with the North Koreans on possible outcomes.

After mulling the rhetoric for the past week, White House officials now believe Kim was attempting to test Trump's willingness to make concessions ahead of the summit, according to a US official. The North's furious denouncement of Bolton is viewed as an attempt to sow divisions among Trump's team, particularly as Bolton and Secretary of State Mike Pompeo have aired differing views of the summit's goals in public.

Trump, meanwhile, has expressed a belief the harsher language was prompted by Chinese President Xi Jinping, who met with Kim in the northeastern Chinese city of Dalian shortly before the new tone emerged. Trump has told aides he believes Xi is attempting to influence the summit, and the matter has become entwined in the ongoing trade standoff between Washington and Beijing.

On Monday, Trump tweeted that China must maintain its pressure on its neighbor ahead of any potential deal.

"China must continue to be strong & tight on the Border of North Korea until a deal is made. The word is that recently the Border has become much more porous and more has been filtering in. I want this to happen, and North Korea to be VERY successful, but only after signing!" he wrote.