(CNN) President Donald Trump is dipping into his playbook of distraction and denial, but even his skills at weaving alternative narratives cannot disguise the growing threat he faces from special counsel Robert Mueller.

On Saturday, Trump announced the exit of chief of staff John Kelly, dismissed new revelations from the Russia probe, slapped familiar foes and promoted violent demonstrations challenging his erstwhile friend, French President Emmanuel Macron.

But while he can spin new stories for the media to chase, the President seems powerless to stop Mueller's relentless focus on his own conduct in the 2016 campaign and ever since.

A week of legal filings related to the Russia investigation has only increased the President's vulnerability and raised new questions about whether his campaign cooperated with a Russian election meddling effort.

The more Mueller's work seems to uncover contacts with Russians by people inside Trump's orbit and evidence that they lied about what happened, the more the President argues that he is being vindicated and cleared.

"We're very happy with what we're reading because there was no collusion whatsoever," Trump told reporters before heading to the Army-Navy football game in Philadelphia.

Trump tweeted earlier Saturday that it was "time for the Witch Hunt to END" and quoted Fox News correspondent Geraldo Rivera, saying "this is collusion illusion" and "there is nothing impeachable here."

"This is collusion illusion, there is no smoking gun here. At this late date, after all that we have gone through, after millions have been spent, we have no Russian Collusion. There is nothing impeachable here." @GeraldoRivera Time for the Witch Hunt to END! — Donald J. Trump (@realDonaldTrump) December 8, 2018

The President has a long record of disregarding evidence that contradicts his preferred version of events. And Trump has mounted a long campaign to discredit the special counsel, apparently seeking to devalue any eventual conclusions that are critical of his conduct.

But the deepening record of the Mueller investigation is raising the possibility that Trump's talent in creating alternative realities is facing its stiffest test yet.

New and damaging information for the White House comes at a time when every move by Mueller appears to bring his investigation deeper into the White House and Trump's inner circle, and shows it has expanded well beyond what may or may not have happened in the 2016 campaign.

So the President has every reason to change the subject.

Kelly's departure has long been expected given an apparently fractious relationship with the President and his diminishing influence in a riotous White House he once tried to tame with military-style discipline.

"I appreciate his service very much," Trump said, of a respected retired general who also served as his first homeland security secretary.

CNN's Kaitlan Collins reported Saturday that Trump was in talks with Nick Ayers, who current serves as chief of staff to Vice President Mike Pence, to succeed Kelly. But the elevation of Ayers is not certain, as he is looking to move his young family back to Georgia and may only want to do the job in the short term.

Trump also took time to tweet about violence in France that has rocked the Macron government and caused the cancellation of fuel tax increases designed to wean consumers off fossil fuels that cause global warming.

"Very sad day & night in Paris. Maybe it's time to end the ridiculous and extremely expensive Paris Agreement and return money back to the people in the form of lower taxes?" Trump wrote on Twitter.

Deepening jeopardy

Taunting a fellow world leader who was once a friend but has recently criticized the President's nationalistic worldview might be a pleasant diversion for Trump, but cannot change the reality of the widening special counsel probe.

Mueller is clearly now looking not just at allegations of possible cooperation of Trump associates with Russia's efforts to interfere in the 2016 election, but at possible obstruction of justice even after the firing of then-FBI Director James Comey in May 2017. That much became clear when CNN reported on Friday that the special counsel has spoken to Kelly in recent months. The chief of staff did not even take the job until July 2017.

A series of filings and court action this week by Mueller, federal prosecutors and attorneys for the President's former lawyer Michael Cohen and former national security adviser Michael Flynn appeared to significantly sharpen the threats facing Trump and key associates.

None of the documents amount to criminal action against the President himself. But they tell an indirect tale of allegedly questionable behavior by the then-GOP nominee.

For the first time, prosecutors said Trump directed Cohen to make payments designed to silence women who claimed affairs with Trump, which broke campaign finance laws.

Mueller also drew a link between Trump's business interests and the Russian election meddling effort. He pointed out that work on a proposed Trump Tower Moscow project that continued until deep into the campaign in June 2016 -- and which Cohen lied about -- came "at a time of sustained efforts by the Russian government to interfere with the US presidential election."

Mueller also confirmed that he has benefited from substantial cooperation from Cohen and Flynn, and that he has documentary evidence in addition to testimony from witnesses. This raises the likelihood that he has built a comprehensive picture into what went on in the Trump campaign, the transition and in the White House, even though he is yet to reveal everything publicly in heavily redacted documents.

Trump and his legal team insist, however, that the President is in the clear.

"When you look at what was revealed today, there's nothing that links the President to collusion with the Russians, so maybe they should fold up their tent, give a report to the Justice Department and go home," Trump's attorney Rudy Giuliani told CNN's Pam Brown on Friday.

Giuliani also said the President never told Cohen to pay women who claimed affairs with him, adding that such payments would not count as a campaign contribution.

The depth of the President's legal and political difficulties will only become clear when Mueller files a final report -- and Trump's team will have the chance to challenge his findings and make their defense. But it's increasingly looking like the President's denials and distractions are failing to keep up with the special counsel's accelerating pace.