WASHINGTON (CNN) -- A reeling White House has no obvious path out of one of the most intense self-imposed crises in modern political history, as the shockwaves of President Donald Trump's firing of FBI Director James Comey intensify.

Six days on, the administration is dealing with damaging consequences of that decision. The White House staff faces a credibility crisis following their shifting explanations for Comey's dismissal. Republican leaders in Congress are dealing with another unwelcome controversy ignited by their President. And Democrats are on offense, sensing an opening ahead of midterm elections next year.

It's nothing new that Trump is unleashing disruption and discord -- that's been his style all along.

But Comey's dismissal during his investigation into Trump's campaign over alleged links to Russian election meddling took the sense of political dislocation in the capital to new extremes.

Trump is suddenly fighting off accusations that he abused his power and even put himself in legal and constitutional jeopardy, with his Republican allies under fire for not doing more to rein him in.

Former Director of National Intelligence James Clapper leveled a striking charge on Sunday, telling CNN's Jake Tapper that he thinks US institutions are under assault from Trump.

"The founding fathers, in their genius, created a system of three co-equal branches of government and a built-in system of checks and balances," Clapper said on "State of the Union."

"I feel as though that is under assault and is eroding."

The White House's current political woes are a direct result of Trump's own actions, and he is showing no sign of changing his approach.

Frustrated, angry and preoccupied by the trajectory of his presidency, Trump is staying true to his instincts, lashing out and trying pursue his own unpredictable course.

"It's the outsiders who change the world and who make a real and lasting difference," Trump said at a commencement address Saturday.

"The more that a broken system tells you that you're wrong, the more certain you should be that you must keep pushing ahead, you must keep pushing forward."

Searching for Comey's replacement

Trump's suggestion Friday that there may be "tapes" of his conversations with Comey further exacerbated the sense of crisis gripping Washington.

In the short term, the furor is complicating his search for a new FBI chief, one he told reporters Saturday he hopes to finish this week.

The President must find someone who has the confidence of the bureau's rank and file, is willing to serve under intense political pressure from his own White House and can win Senate confirmation.

The West Wing staff must negotiate this daunting assignment with their own fates in question, amid rampant rumors of a major personnel shakeup after Trump sabotaged efforts of his own team to explain the Comey firing.

At least six candidates headed to the Justice Department on Saturday, including former Assistant Attorney General Alice Fisher, special agent Adam Lee, acting Director Andrew McCabe, Sen. John Cornyn of Texas and judges Michael Garcia and Henry Hudson.

But former CIA Director James Woolsey told CNN's Fareed Zakaria that it will be tough finding someone willing to serve.

"I think it's going to be very hard to find a good FBI director who is willing to operate under the circumstances that we've seen this week," Woolsey said in an interview Sunday.

Democrats, meanwhile, offered a glimpse of the campaign they are preparing to wage to complicate Trump's search for a replacement.

Senate Minority Leader Chuck Schumer said Sunday that the Senate should refuse to confirm a new FBI director until the Justice Department appoints a special prosecutor to probe allegations of collusion between the Trump campaign and Russia.

Schumer also insisted the the nominee should not be a "partisan politician" and should be willing to stand up to White House pressure.

But he admitted that Democrats would need help in imposing meaningful constraints on Trump's search.

"The key here, of course, is getting some of our Republican colleagues to join us," Schumer told CNN's Tapper on "State of the Union."

One of those colleagues is South Carolina Sen. Lindsey Graham, who on Sunday criticized the White House for first claiming that Comey was fired over his handling of the Hillary Clinton email saga before Trump told NBC Friday that he ousted the FBI chief over the Russian investigation.

"The President has a chance to clean up the mess that he mostly created," Graham said. "He really, I think, did his staff a disservice by changing the explanation."

Graham also said that if any tapes exist, Trump needs to turn them over, and added that the situation demands that senators take further steps.

"I think it requires somebody like me, a Republican, to call Comey before the (Senate) Judiciary Committee," he said, adding that Trump should "back off" from commenting or tweeting about the investigation.

Graham is not alone among Republicans in expressing concern. But so far, the most important figures -- Senate Majority Leader Mitch McConnell and House Speaker Paul Ryan -- are resisting demands for a special prosecutor or congressional committee to probe alleged Trump campaign ties with Moscow.

Clouds over Trump's first foreign trip

Given the political storm that raged over the weekend, it is difficult to see how the White House could reset the political mood. But Trump's crucial first foreign trip, which begins when he heads for Saudi Arabia Friday, will give him a chance to try to change the subject.

The four-nation journey was already a daunting assignment: It marks the first venture abroad for a commander in chief who lacks any diplomatic experience and is viewed with great uncertainty by many US allies.

Trump will meet the leaders of the United Arab Emirates, Turkey and Colombia in Washington this week before heading to Saudi Arabia, Israel, Italy and Belgium.

"This trip is truly historic. No president has ever visited the homelands and holy sites of the Jewish, Christian and Muslim faiths all on one trip," said national security adviser H.R. McMaster, briefing reporters on Friday.

"What President Trump is seeking is to unite peoples of all faiths around a common vision of peace, progress and prosperity. He will bring a message of tolerance and of hope to billions, including to millions of Americans who profess these faiths. The President will focus on what unites us," he said.

Given the events of the previous days, McMaster's message seemed incongruous, as he portrayed a President who had just ignited discord at home as a unifying force abroad.

But at times, McMaster, in a stentorian performance, almost seemed to be willing the administration onto better political ground with the strength of his rhetoric. Administration officials may hope that by getting Trump out of Washington for a week or more, they may help cool the political storm raging around the White House.

McMaster's prominent role may be a message to allies abroad, following reports in Washington last week that Trump was tiring of him. Diplomats from a number of foreign nations have said that they view McMaster and other prominent administration foreign policy hands -- including Defense Secretary James Mattis -- as a source of stability and continuity even amid the wild swings of Trump's leadership.

But if the White House hopes that a trip abroad can cure its problems, it could be in for a shock. Foreign tours, with their jet-lag, tedious diplomatic summits and intense media glare, impose their own demands on a President, especially one as inexperienced as Trump.

With that in mind, former Defense Secretary Robert Gates suggested Sunday on CBS News' "Face the Nation" that the President should drop the unpredictable, improvisational approach overseas that has led him into such controversy at home.

"I think when it comes to the issues," Gates said. "I'd advise him to stick to the script."

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