And it suggests that Cohen, who paid off adult film star Stormy Daniels, could be a bridge between the two separate legal strands threatening Trump.

"There is no way that they are looking for things that don't connect to the President in some way," Anne Milgram, a former New Jersey attorney general told CNN's Anderson Cooper of the Cohen raid. "It really is an unbelievable day when you start to think about what is happening, what we are going to see next."

Trump's rage continued into Tuesday morning, when he tweeted that "Attorney--client privilege is dead!" and referred to a "A TOTAL WITCH HUNT!!!," his preferred moniker for Mueller's investigation.

'Pretty treacherous territory'

It was an extraordinary day that going forward may significantly lessen the chances that America escapes the maelstrom of Mueller's special counsel investigation and Trump's consequent fury without significant damage to its civic institutions.

"We are in pretty treacherous territory here. It's unprecedented to my knowledge to have the President's personal attorney raided like this," said CNN senior political analyst David Gergen. "They must have been able to present evidence that was hugely compelling to take a step like this."

Sources inside the White House say that Trump sees the move against Cohen as proof that Mueller has leaped far beyond the constraints of his original probe into whether his campaign operatives colluded with Russia.

The fact that Cohen -- a relentless, unyielding protector of Trump -- was hit by a search warrant particularly fed Trump's anger.

"It's a disgrace, it's, frankly, a real disgrace, it's an attack on our country in a true sense. It's an attack on all we stand for," Trump told reporters at the White House.

The FBI raids were based on search warrants obtained by a federal judge via the US Attorney of the Southern District of New York, Geoffrey Berman, a Trump appointee. Sessions has recused himself, but federal guidelines suggest Rosenstein would have signed off on Mueller's referral.

Trump's extreme anger at Sessions and Rosenstein, written across his face as he fulminated in front of reporters at the White House, means it is not far-fetched to consider he may be thinking the unthinkable -- launching a stunning maneuver to topple the leadership of the Justice Department that would enable him to effectuate the canning of Mueller.

"Why don't I just fire Mueller? Well, I think it's a disgrace what's going on. We'll see what happens," Trump said. "But I think it's really a sad situation, when you look at what happened. And many people have said, you should fire him."

Trump could have been simply venting, in a televised version of the Twitter rants that he has often used to slam the FBI, the Mueller probe and the integrity of those who are leading the investigation against him.

If that is the case, perhaps he got it off his chest while attempting to limit the impact of Monday's news on his ever-loyal political base following a months-long effort to discredit Mueller's investigation and the FBI.

Stuck in a corner?

JUST WATCHED Bharara: Raid approved by people Trump picked Replay More Videos ... MUST WATCH Bharara: Raid approved by people Trump picked 01:37

Yet Trump's demeanor gave the impression that he was stuck in a corner, contemplating extreme measures to extricate himself and may be beyond convincing otherwise.

He didn't look like someone content to sit tight and await Mueller's results.

One source familiar with Trump's mood told CNN's Gloria Borger that Trump was more angry with Rosenstein and Sessions than Mueller, and that no one around him knew what he would do next.

CNN's Kaitlan Collins reported that the Cohen raid sent Trump over the edge because the lawyer is like a surrogate family member for Trump, and frequently dines with the President and first lady Melania Trump.

Should Trump orchestrate the firing of Mueller, he would unleash a political tsunami and trigger demands for impeachment by Democrats. Republicans who run Congress would face extreme pressure to consider whether the President's actions merit such draconian action. There's no way out of that imbroglio without causing significant political reverberations that would last for years.

Trump's presidency has been packed with surreal moments. But Monday's staggering events took some believing.

An FBI raid on the offices of a lawyer employed by a sitting President is something that is without precedent in modern political memory.

A President reacting in real time by attacking the probity of an investigation against him and wondering how to end it.

And even the setting of Trump's comments was mind-boggling -- he burst out with his comments unprompted as his top military brass was gathered around him, contemplating whether to send US forces to war in Syria.

If Monday's events bore threatening implications for the President -- they also considerably raise the stakes for Mueller himself. While the special counsel may have only referred the Cohen case to New York prosecutors he is now indelibly linked to the move in a way that could impact the political environment in which his investigation is unfolding.

"I think it's a bet and they better find something," said Mike Shields, a former chief of staff of the Republican National Committee, arguing that a decision to raid the office of the President's personal lawyer raises the stakes for his investigation.

"You don't find anything -- the credibility of the entire investigation is going to rest on that. ... It is going to make (Mueller) look terrible if nothing comes out of it," Shields said on CNN.

But Preet Bharara, who served as the US Attorney in the Southern District of New York until he was fired by Trump, suggested that prosecutors would not undertake such an aggressive move lightly.

"It's being done because people think it's very serious, people think it's totally warranted and people think there's evidence of a significant enough nature that you're going to risk doing something sensitive like raiding a law office," Bharara said.

CLARIFICATION: This story has been updated to reflect that federal guidelines indicate Deputy Attorney General Rod Rosenstein would have signed off on Robert Mueller's referral to the US attorney's office.