The requests came after news reports revealed Trump's disclosure of highly classified material to Russian officials and an alleged attempt to shut down an investigation into his former national security adviser, Michael Flynn. Tomorrow, Deputy Attorney General Rod Rosenstein will brief the full Senate on Comey's firing.
Today, some members of the GOP began predicting that the party will rally behind some sort of independent investigative body to probe the two issues.
Congressman Charlie Dent, co-chairman of the moderate Tuesday Group, said today that the collective political fallout from the past week "will make it difficult" for Republicans to resist a change in approach.
Dent said he does not like investigations by independent prosecutors because they "tend to take on a life of their own" and instead preferred an independent commission of outside experts.
"We may have to move in that direction," Dent said at a forum moderated by Centre Forward, a moderate Democratic organisation.
The collision of the two stories yesterday left Republicans reeling, with a senior GOP senator comparing the situation to Watergate, and Speaker Paul Ryan directing the House Committee on Oversight and Government Reform to immediately seek records from the FBI.
Ryan was careful to strike an evenhanded tone today, saying congressional committees would continue to conduct oversight "regardless of what party is in the White House" but seeming to dismiss some concerns that have arisen in the wake of news about a memo by Comey suggesting that Trump had pressured him to drop the Flynn investigation.
"There's clearly a lot of politics being played here," Ryan said.
He noted FBI acting director Andrew McCabe's recent comment that there has been "no effort to impede our investigation". McCabe made the remark in a congressional hearing when asked whether the firing of Comey had affected the bureau's work.
Ryan also sounded a sceptical note about Comey's actions after the meeting in which Trump allegedly asked him to "let this go," referring to the Flynn probe.
"If this happened as he described, why didn't [Comey] take action at the time?" Ryan said.
Senate Majority Leader Mitch McConnell, has not directly commented on allegations that Trump tried to pressure Comey. He did not mention the President or the controversies facing the White House during his morning remarks on the Senate floor and ignored questions from reporters in the halls of the Capitol.
Senator John McCain compared the current situation to the Watergate scandal while speaking at an International Republican Institute dinner.
"We've seen this movie before. I think it's reaching the point where it's of Watergate size and scale and a couple of other scandals that you and I have seen," McCain told Bob Schieffer of CBS News. "It's a centipede, and the shoe continues to drop."
Asked today whether the imbroglio could lead to impeachment, McCain responded: "I have no idea on that - come on".
The senator's spokeswoman, Julie Tarallo, said the comparison was "simply meant to convey that the constant revelations of events surrounding Russia's interference in the 2016 election are reminiscent of past scandals, are not good for America, and require further scrutiny".
When asked what he'd say to Trump, McCain replied: "Get it all out. It's not going to be over until every aspect of it is thoroughly examined and the American people have made a judgment. And the longer you delay, the longer it's going to last."
Other Republican senators, while saying they need to review documents before making a final judgment, voiced doubts about Trump.
"There's a lot here that's really scary," Senator Ben Sasse said in an interview with conservative radio host Hugh Hewitt. "It's obviously inappropriate for any president to be trying to interfere with an investigation."
Senator Susan Collins, a member of the Intelligence Committee, and Senator Lisa Murkowski reissued calls for the Justice Department to consider appointing a special prosecutor to probe Russia's election interference.
Republican Senator Patrick Toomey is calling for a Democrat to replace Comey as head of the FBI. Toomey believes "changes are needed at the White House," spokesman Steve Kelly told the Washington Post .
And one of two House Republicans to endorse an independent investigation of the Comey matter said that if the details reported this week are true, it could be grounds for impeaching Trump. "Yes," replied Congressman Justin Amash of Michigan, a member of the Oversight Committee, when posed the question by a reporter.
The White House has been largely silent since the New York Times first reported on Trump's alleged effort to end the Flynn investigation by pressuring Comey. Trump aides have not directly commented on the story and were absent from television shows starting yesterday, a notable difference from last week, when they blanketed the networks to defend Comey's firing.
Before the New York Times story broke, Trump aides had sought to tamp down the controversy over Trump sharing classified information with Russian officials. National security adviser H.R. McMaster called the action "wholly appropriate" to the conversation that occurred in the Oval Office.
Both Republicans and Democrats have called on Trump, who has suggested that he records his conversations, to provide a transcript of the meeting to congressional intelligence committees so they can assess what took place.
White House aides have neither confirmed nor denied the possibility that Trump keeps tapes of his meetings.
Democrats blasted House Republicans for doing little to probe Trump's potential ties to Russia.
"They do as little as humanly possible just to claim that they're doing something," said Congtressman Elijah Cummings of Maryland, the ranking Democrat on the Oversight Committee.
"Our committee should already be conducting robust and transparent investigations," said Cummings, who joined 32 other Democrats in calling for his panel to partner with the Judiciary Committee on a new probe of Trump's White House.
"Speaker Ryan has shown he has zero - zero, zero - appetite," the Democrat said.
Democrats' priority is advancing a bill from Congressman Eric Swalwell, creating a bipartisan congressional commission to investigate Russia's cyberintrusions, how the intelligence community handled the matter and the president's potential involvement.
The Democrats are hoping to file a discharge petition - which requires the signatures of a majority of all House members - to compel GOP leaders to schedule a vote on the proposal. But they could have trouble gathering enough support: As of today, the Post found only five GOP senators and 10 House Republicans open to some kind of independent investigation.
While several Democrats have called for Trump to be impeached over the Comey firing, the party's leaders reiterated that their priority was a special investigation.
Congressman Adam Schiff cautioned that hasty talk of impeachment would distract from the need for a bipartisan probe - and mire the investigation in partisanship.
"It cannot be perceived as an effort to nullify the election by other means," he said.
Some rank-and-file Republicans dismissed the controversies out of hand.
"It's being made a bigger deal than what it is," Congressman Barry Loudermilk said, maintaining that leaks to the media were a more serious matter.
Trump "doesn't fit the model of a typical politician, and that's what the real issue is here. He's a business guy, and he wants to get things done".
Congressman Robert Aderholt also was unperturbed by the latest reports. Back in Alabama, he said, there is "a lot of frustration that they're not allowing him to do his job".
"So far I have not seen anything that's that alarming," Aderholt said.
