(CNN) When President Richard Nixon ordered the firing of Watergate special prosecutor Archibald Cox in 1973, he failed to drive a stake through the heart of his investigation. Propelled by appointment of a new prosecutor, congressional fortitude and public outrage, the Watergate probe continued.

That was then.

Today, the political atmosphere is different enough that if President Donald Trump triggers the firing of special counsel Robert Mueller, the fate of the Russia investigation would be thrown in doubt.

Trump has increased his attacks against Mueller's investigation since Monday when the FBI raided the office of his personal attorney Michael Cohen at the referral of the special counsel's office. The President's outbursts during a White House meeting and on Twitter have fueled new speculation that he could seek to remove Mueller.

The increasing speculation over what Trump might do naturally leads to what would happen to the wide-ranging probe into Russian interference in the 2016 election if the man leading everything is sacked. Multiple Republican lawmakers have warned Trump against sacking Mueller, including Sen. Jeff Flake, who in March invoked the potential of an impeachment "remedy" if Trump does so.

The investigation would remain within Justice Department, as Mueller's is now. But the apparatus intended to ensure independence from the White House -- that is, a specially appointed counsel operating with his own team -- could be dissolved.

Any DOJ official who ensured the firing of Mueller, at Trump's request, would likely be the one deciding how vigorously to continue the Russia probe within the department. That official -- presumably a new acting attorney general -- could also appoint a new special counsel, as happened in 1973.

Related congressional oversight and state prosecutions would remain, but those efforts pale compared to the force of federal efforts to prosecute crimes related to Russia's intrusion on US democracy and any Trump campaign connection.

Then there's a larger issue of a congressional check on Trump that makes the current situation different from what Nixon faced.

Back 45 years ago, a Democratic majority on Capitol Hill led the investigation into Republican Nixon's cover up of the burglary at the Watergate building of the Democratic national headquarters. Nixon's ultimate downfall in 1974 came as Republican leaders such as Arizona Sen. Barry Goldwater pressured him to resign.

Republicans control both the House and Senate today, and the party's leaders haven't been especially critical of Trump's attacks on Mueller, even as they recently said the special counsel should be allowed to proceed.

"Don't create a constitutional crisis. Congress cannot preempt such a firing. Our only constitutional remedy is after the fact, through impeachment. No one wants that outcome. Mr. President, please don't go there," Flake tweeted in March.

Clock ticking for Trump?

As speculation that Trump would seek Mueller's dismissal intensified in the halls of Congress and elsewhere this week, the motive behind the President's new attacks on the special counsel -- he called the Mueller investigation "an attack on our country" and repeated his "WITCH HUNT" claims on Twitter -- are unknown.

It could be primarily to discredit its work in the American mind. Or the President may be feeling new pressure in the wake of the FBI raid on Cohen.

He may also hear the clock ticking.

With each passing day comes the possibility of additional indictments and, nearer in sight, the fall elections, when Democrats have a chance to win a majority in the US House of Representatives. If that happens, Democrats would have a new ability to investigate the Republican President and challenge his policies.

White House officials insist that Trump does not intend to seek the dismissal of Mueller, who was appointed in May 2017 after Trump fired FBI Director James Comey, then overseeing the Russia probe.

Former prosecutors and legal analysts disagree about the fallout of a possible firing of Mueller, who led the FBI first during the administration of Republican President George W. Bush and then Democratic President Barack Obama.

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"Bob Mueller is a towering figure, a former Republican-appointed FBI director, uniformly respected by officials. He is irreplaceable in this role," said Ronald Weich, a former federal prosecutor, Justice Department assistant attorney general, and now dean of the University of Baltimore law school.

Harvard law professor Jack Goldsmith, also a former assistant attorney general, does not believe the situation would be so dire, if it comes to that. He predicted that current FBI Director Christopher Wray would continue the Russia investigation and that a new special counsel would be named.

Goldsmith also emphasized the legal hurdle Trump faces. "If Trump wished to stop the Mueller investigation, he couldn't just tweet a declaration that it is over," Goldsmith wrote in a Lawfare column earlier this year.

Goldsmith referred to the Department of Justice regulation that would cover any dismissal. It says that the attorney general (or acting attorney general) may remove the counsel only for "misconduct, dereliction of duty, incapacity, conflict of interest, or for other good cause, including violation of Departmental policies," and must state the reasons in writing.

Justice Department institutional interests could make it difficult for Trump to kill the investigation. Even before Mueller's appointment last May, the FBI was looking into Russia's interference in the 2016 election.

Mueller has continued to work with other federal agencies and state prosecutors, including New York Attorney General Eric Schneiderman.

He has also worked with the US attorney for the Southern District of New York, Geoffrey Berman, which executed the search warrants at Cohen's office.

If the special counsel is removed, the future of those pending actions would be determined by DOJ officials.

What about Manafort and other cases?

Since taking over from Comey last year, Mueller has charged 19 people, most significantly 13 Russians for their use of social media during the campaign, former Trump national security adviser Michael Flynn and Trump campaign chairman Paul Manafort. Manafort faces five federal criminal charges in Washington, including conspiracy money laundering and foreign lobbying violations, and 18 federal charges in Virginia, largely related to alleged bank fraud (he denies all charges).

Manafort's former deputy and business partner Rick Gates agreed in February to cooperate with Mueller after pleading guilty to two criminal charges. Flynn in December pleaded guilty to lying to the FBI about conversations with Russia's ambassador and is also cooperating. George Papadopoulos, a former campaign foreign policy adviser has also pleaded guilty to making a false statement to the FBI. He lied about his interactions with foreign nationals, including people with ties to the Russian government.

A California man, Richard Pinedo , also agreed to cooperate with Mueller's team in exchange for pleading guilty to identity fraud.

Last week, Alex van der Zwaan , a Dutch lawyer with ties to Gates and Manafort, became the first person to be sentenced in Mueller's investigation after he admitted to lying to investigators and failing to turn over emails in February.

If Mueller were no longer on the case, the fate of the Manafort prosecution would fall to the DOJ officials who take over the probe.

As Mueller's team has been working steadily, special committees on Capitol Hill have also been looking into the Russia election meddling. If Mueller's team would fold, members of Congress would have the power to subpoena documents from the Justice Department. But even if they discover previously undisclosed wrongdoing, congressional committees lack any prosecutorial power.

Beyond the fate of the current wide-ranging investigations and pending prosecutions is a power that Trump alone does wield. That is the pardon power.

Last August, over great public protest, he pardoned former Arizona sheriff Joe Arpaio, who faced a jail sentence for criminal contempt related to his crackdown on immigrants.

It is difficult to predict what Trump would ultimately do about Mueller. But Trump has already signaled he would not shy from a politically unpopular pardon of someone caught up in Mueller's probe.

Editor's Note: This story has been updated following the raid on Trump lawyer Michael Cohen. It originally appeared on March 21.