(CNN) Like all of President Donald Trump's enemies, Kim Jong Un now has a catchy nickname -- "Rocket Man."

Trump will always be Trump, no matter international protocol or the gravity of a national security crisis.

Yet mocking Kim, as Trump did on Sunday in a tweet, cannot disguise a sobering reality that the North Korean dictator is winning his race to twin a nuclear bomb and a long-range missile that could hit US soil. Meanwhile, White House aides who have said that diplomacy is the preferred US option are talking tough -- escalating their rhetoric as Trump debuts at the United Nations General Assembly.

"If North Korea keeps on with this reckless behavior, if the United States has to defend itself or defend its allies in any way, North Korea will be destroyed," US envoy to the UN Nikki Haley said on CNN's "State of the Union" on Sunday.

Despite using an Elton John hit to demean Kim, Trump, who critics say has worsened the crisis with his ad-libs, chose not to further inflame the situation on Monday.

"I think most of you know how I feel. We'll see what happens," Trump said as he arrived at the UN.

Yet there are reasons to question whether Trump's barbs or his administration's saber-rattling are likely to be effective in slowing Kim's nuclear march -- or are even a true expression of where the White House stands on its diplomatic effort.

Inadequate?

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First, Trump's rhetoric has proven so far inadequate to change Kim's calculations.

Since his warning that he would rain "fire and fury" over North Korea, the isolated state has sent two missiles over the territory of US ally Japan and detonated its mightiest nuclear test.

Though it inherited the crisis from previous administrations who were also unsuccessful in thwarting the isolated state's nuclear drive, nothing the Trump administration has tried so far has worked.

Whether it has been passing more UN sanctions, warning time is almost done for diplomacy, staging military maneuvers, demanding action from China or threatening to reduce North Korea to dust, Kim has continued to trample US red lines.

For instance, South Korea's Defense Ministry said Monday that North Korea has claimed its development of an Intercontinental Ballistic Missile (ICBM) has advanced "near the final stage."

Pyongyang, meanwhile, warned that it was a "foolish dream" to think that new UN sanctions passed last week targeting some oil imports and its exports would stop it from becoming a fully fledged nuclear power.

Given Kim's actions, and the fact that the nuclear program is a crucial ingredient of the personality cult and narrative of US aggression that sustains his regime, there is every reason to believe the foreign ministry's warnings.

And since the US position is that any talks with the North must start from the premise of denuclearizing the peninsula, hopes of kindling an opening directly with the North Koreans seems futile.

There is another reason to question whether the administration has really reached the end of its rope on pressing the UN to act on North Korea.

On Friday, while Haley and national security adviser H.R. McMaster both said that time was running short for diplomacy, they also urged time for sanctions to work, and called for rigorous enforcement.

Their comments seemed as much an attempt to get the rest of the world to show the urgency that is obvious in Washington but does seem lacking elsewhere as an indication that war was imminent.

Grave consequences

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Military threats may also not be exactly what they seem.

While top US officials are increasingly saying they are happy to turn the problem over to US Defense Secretary James Mattis, the Pentagon has yet to explain clearly how the grave consequences that have always augured against a military solution have changed.

For instance, it appears unlikely that for all Trump's warnings that US forces are "locked and loaded" that the US could identify and destroy all of Kim's nuclear arsenal, missile stocks and artillery pieces in an initial attack. Failure to do so could cause horrendous civilian casualties in North Korean reprisal attacks against South Korea, Japan and against US soldiers in both nations.

Until the Pentagon can solve that conundrum, some observers will take US military threats with a pinch of salt -- unless they conclude that Trump is ready to accept a huge humanitarian toll in Asia -- to keep America safe from North Korea.

One possible interpretation of the harsh turn in US rhetoric is that it is intended to heap more and more pressure on China and Russia -- two states that have leverage with the North Koreans that has not yet been fully deployed.

Though Chinese President Xi Jinping and Russian President Vladimir Putin are not at UNGA, the timing may also have something to do with leaders gathering at the UN headquarters with the eyes of the world on foreign policy.

If the US is really "out of time" on North Korea's nuclear program, as McMaster told reporters at the White House, Washington would be expected to soon move to one of its most strident, yet risky options -- targeting Chinese firms and banks that do business with North Korea, on the open or black market.

The threat of such action could be intended to change China's view of the situation and to get it to sign up to more punitive sanctions.

Such sanctions would effectively offer Chinese firms a choice of trading with the US or North Korea. But given the opacity of Chinese politics -- at a crucial time, ahead of the Communist Party's Congress, a once-in-five-year event -- such a critical step is not guaranteed to change Beijing's mind and could trigger reprisals against the US.

There is also the question of inclination.

China is responsible for most of North Korea's oil imports and Russian firms are the largest employers of North Korean forced laborers whose salaries swell Pyongyang's revenues.

It is not a clear cut case that either Russia or China is ready to relieve Washington of one of its most intractable foreign policy problems, and given differences with the US elsewhere may have an incentive to keep Trump on the hook.

Neither nation has an interest meanwhile in any kind of regime targeting strategy by Washington that could topple Kim's government, create massive refugee flows and instability -- and could eventually produce a unified Korea that leans closely to the US than its neighbors to the North.

The White House said Trump spoke to Xi on the phone on Monday and won an undertaking for rigorous enforcement of existing sanctions on North Korea.

But there was no word on any follow on action by China.