Republican lawmakers on Wednesday argued that the conviction and guilty plea of two former Trump aides are not a major congressional concern because they are not related to allegations that the campaign colluded with Russians, while Democrats said the president's implication in a crime should result in a delay in confirmation hearings for his Supreme Court nominee.

On Tuesday afternoon, Trump former campaign chairman Paul Manafort was found guilty on eight felony counts in his bank and tax fraud trial in Virginia, while the president’s former personal lawyer Michael Cohen pleaded guilty in New York to tax evasion, bank fraud and campaign finance violations, telling the court he made hush-money payments to women at Trump’s direction.

Some Democrats said Wednesday that in the wake of Cohen's plea, they would not be meeting with Judge Brett Kavanaugh ahead of his confirmation hearings.

"The fact that a sitting president is an unindicted co-conspirator in a criminal situation, you know what, I am canceling, I will be canceling my appointment with Judge Kavanaugh because I choose not to extend courtesy to this president who is an unindicted co-conspirator," said Sen. Mazie Hirono, D-Hawaii.

"I will not take a meeting with Brett Kavanaugh. He has been nominated by someone implicated, and all but named as a co-conspirator, in federal crimes," tweeted Sen. Ed Markey, D-Mass. "His nomination is tainted and should be considered illegitimate."

Several other Senate Democrats said that in light of Tuesday's news, Kavanaugh's confirmation hearings themselves should be put on hold.

“The possibility of criminal wrongdoing by the president, combined with existing doubts that Brett Kavanaugh believes a president can even be investigated, demand further review of this situation. Brett Kavanaugh’s hearing should be delayed," Dianne Feinstein, D-Calif., the ranking member of the Senate Judiciary Committee, said in a statement on Wednesday.

Sen. Kamala Harris, D-Calif., told MSNBC’s “Andrea Mitchell Reports” on Wednesday that she did not support the Senate holding a nomination hearing for Kavanaugh, because Cohen had implicated the president in a crime and the Supreme Court could possibly weigh in on the case.

“As it relates to the Kavanaugh nomination and the hearings that are scheduled to happen in just two weeks, I would suggest that an unindicted co-conspirator to a crime should not be in the business of having the ability to appoint someone to a lifetime position on the highest court in our land, a court which, invariably, would hear the matters that are the subject of this very discussion,” she said.

Sen. Jeanne Shaheen, D-N.H., said that the possibility that the Supreme Court would be asked to rule on a related case involving Trump meant Congress needed a clear view of Kavanaugh's views on executive power.

"In light of yesterday's events, the Senate should delay hearings on Kavanaugh's nomination to the Supreme Court," she said in a statement Wednesday. "There must be checks and balances on this President. To that end, the Senate should be provided all necessary records related to Kavanaugh's nomination, particularly those that indicate his views on executive power."

Senate Minority Leader Chuck Schumer, D-N.Y. also called for a delay in the hearings. "Judge Kavanaugh’s refusal to say a POTUS must comply w a duly issued subpoena & Mr Cohen’s implication of POTUS in a federal crime make the danger of Kavanaugh's nomination to the SCOTUS abundantly clear," Schumer said in a tweet on Wednesday. "It's a game changer & Chairman Grassley should delay confirmation hearings."

Trump nominated Kavanaugh, a federal appeals court judge in Washington, in July to succeed Justice Anthony Kennedy on the Supreme Court.

George Hartmann, a spokesman for Sen. Chuck Grassley, R-Iowa, who is the chair of the Senate Judiciary Committee, said in a statement on Wednesday that Kavanaugh's nomination will go on as planned.

"Calls to delay the hearing are just the latest tactic from opponents who decided to vote “no” weeks ago, frantically looking for anything that sticks. The hearing will begin as planned on September 4,” Hartmann said.

Meanwhile, GOP lawmakers on Capitol Hill publicly downplayed the impact of Tuesday's developments, noting that the convictions were not directly related to special counsel Mueller’s key mandate of investigating allegations of Russian collusion with Trump's campaign during the 2016 U.S. election.

Republican lawmakers who are allies of the president have indicated that their red line for Trump is if Mueller proves that the Trump campaign colluded with Russia.

“I haven't been able to look at all the details, but I would note that none of this has anything to do with the Russian collusion or meddling in the election, which seems to be the main focus and certainly has been the subject of the investigation by the Senate Intelligence Committee that I sit on,” Sen. John Cornyn, R-Texas, said late Tuesday after the news of Cohen’s guilty plea and Manafort’s eight felony convictions.

On Wednesday, Sen. John Kennedy, R-La., struck a similar note. "As best I can tell, there’s nothing in any of the plea agreement or the Manafort trial and jury verdict dealing with Russia," he said. "I’m not saying that not paying your taxes and lying among the application are not serious, they are both very, very serious offenses. But if your question is are we any further along in understanding what happened in the 2016 election? I don’t think we are."

He added that he hadn't seen any evidence to suggest Trump was aware of Cohen and Manafort's crimes.

Sen. Lindsey Graham, R-S.C., who has criticized the president on several past occasions, said late Tuesday that "any time your lawyer is convicted of anything, it's probably not a good day.”

But, he added Trump has said "on endless occasions that he hasn't done anything with Russians, that's really the chief issue."

"Campaign finance violations, I don't know what will come from that, but the thing that will hurt the president the most is if, in fact, his campaign did coordinate with a foreign government like Russia," Graham said. "Anything short of that is probably going to fall into partisan camps.”

Later, he again told reporters that he hadn't seen any signs of Russia collusion: "If that ever proved to be so — and I have seen no evidence of it — that would shake me to my foundation."

Other, more frequent GOP critics of the president took a tougher tone but did not suggest any potential consequences to the president or action by Congress.

Sen. Ben Sasse, R-Neb., blasted Cohen and Manafort in a statement on Tuesday, saying they should not have been near the White House. “Paul Manafort is a founding member of the DC swamp and Michael Cohen is the Gotham version of the same. Neither one of these felons should have been anywhere near the presidency," he said.

Sen. Bob Corker, R-Tenn., said observers of the Trump administration “shouldn’t be surprised” by then-candidate Trump’s actions, adding that in his 11 years in federal office he has “never seen anything like this.”

Sen. Orrin Hatch, R-Utah, said that Cohen's claims about Trump's involvement were "serious charges and they can’t be ignored,” Hatch said. “I don’t think [the president] can be indicted while sitting in office, but we’ll just have to see where this all works out.”

“I’m not very happy about it, I’ll put it that way, and should have never happened to begin with,” he added.

Sen. Patrick Toomey, R-Penn., asked about the president, responded without any direct reference to Trump at all.

“There is no good news in what’s happening,” he said. “Obviously, this is very, very unfortunate, it’s very serious. I want to see this go through our judicial system. That’s what has been happening and we’ll see it through.”

The bottom line, Graham said Wednesday: This news has become "one more problem" Republicans will face in a campaign cycle already littered with political landmines — a distraction from a midterm message focused on their record this session.

"It's just drama away from the agenda that most of us signed up for," he said.