Republicans reserved judgement Tuesday in the wake of a report that President Donald Trump asked then-FBI Director James Comey to drop the FBI's investigation former National Security Adviser Michael Flynn's ties with Russia and Turkey.

"I'm not going to make a decision based on a New York Times story," South Carolina Republican Sen. Lindsay Graham told reporters Tuesday night.

But Democrats responded immediately, with some suggesting such a request from the president would qualify as obstruction of justice.

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The memo's existence, first reported by The New York Times and confirmed by CBS News, came to light only 24 hours after another report that Mr. Trump shared "inappropriate" information with Russian diplomats the day after firing Comey. Flynn was ousted from the White House after he misled Vice President Mike Pence about his contact with the Russian ambassador.

Quietly, however, pressure is building among Republicans to speak up against Mr. Trump. Vermont Democratic Sen. Chris Murphy claimed both Democrats and Republicans on the Senate floor Tuesday night were chattering about the exact definition of obstruction of justice, after news of the memo broke.

A senior GOP congressional staffer who stopped short of calling for a special prosecutor six weeks ago and who had said the Senate Intelligence Committee's ongoing investigation into Russian election meddling was sufficient, told CBS News Tuesday that Washington is on a "path to a special counsel" in the Russia investigation, citing a "crisis of confidence." The source said any effort by the president to pick a new FBI director is "dead in the water," and Congress may want to stick with FBI Acting Director Andrew McCabe.

A source already told CBS News there is a "whole lot of interfering" in the FBI's Russia investigation, an assertion underscored by the existence of Comey's memo.

Democrats, many of whom have already called for a special prosecutor in the Russia probe, intensified those calls on Tuesday.

Sen. Dianne Feinstein, the top Democrat on the Senate Judiciary Committee, who has called for a special prosecutor in the Russia investigation, on Tuesday said she wants the Senate Judiciary Committee to hold a hearing to find out the details surrounding Mr. Trump's reported request to end the Flynn investigation.

"I'm shocked and surprised by this development and would like to discuss it with (Senate Judiciary Committee) Chairman (Chuck) Grassley, and look forward to doing so, Feinstein said. "The Judiciary Committee is the appropriate place to hold a hearing and get to the bottom of exactly what was said and by whom."

Meanwhile, Senate Democratic Whip Dick Durbin said Comey's memo "raises serious questions about obstruction of justice."

"Well, this stunning breathtaking revelation that the president is accused of reaching out directly to the head of the FBI to stop an investigation of Gen. Flynn in these circumstance raises serious questions of obstruction of justice," Durbin told reporters Tuesday night.

"I mean that is the fundamental question here -- is anyone including the president of the United States above the law? Can they all, everyone be held accountable as they should be under the rule of law? And this revelation of this statement that's been alleged really raises that question."

Other Democrats, including House Speaker Nancy Pelosi, reacted to the memo almost immediately on Twitter.

At best, Trump has committed a grave abuse of executive power. At worst, he has obstructed justice. We must #ProtectOurDemocracy. — Nancy Pelosi (@NancyPelosi) May 16, 2017

As frmr prosecutor, I believe an obstruction of justice investigation is warranted. Investigation should not be limited to Intel Committees. — Bill Keating (@USRepKeating) May 16, 2017

This may be the clearest example yet of an effort by President Trump to obstruct justice. Vital that Comey testifies at public hearing soon. https://t.co/tkJnwP9PfV — Chris Van Hollen (@ChrisVanHollen) May 16, 2017

If this report is true, this is obstruction of justice. Congress must subpoena the #ComeyMemos. — Congressman Tim Ryan (@RepTimRyan) May 16, 2017

If Trump asked Comey to stop the Flynn probe, that's clearly obstruction of justice. The president is not above the law. #FollowTheFacts https://t.co/LKeigj6eUM — Rep. Roybal-Allard (@RepRoybalAllard) May 16, 2017

Senate Minority Leader Chuck Schumer, on the Senate floor Tuesday night, told his colleagues, "history is watching."

"In a week full of revelation after revelation," Schumer said. "On a day when we thought things could not get any worse they have. I was shaken by the report in the New York Times that alleged the president tried to shut down an active FBI investigation into a close political associate. And we are only one day removed from stunning allegations that the president may have divulged classified information to a known adversary.

Concerns about our national security, the rule of law, the independence of our nation's highest law enforcement agencies are mounting. The country is being tested in unprecedented ways. I say to all of my colleagues in the Senate history is watching."

Reporting contributed by CBS News' Nancy Cordes, Andy Triay, Jeff Pegues and Alan He