(CNN) Congressional Republicans are largely avoiding speculation that the guilty plea by President Donald Trump's longtime personal lawyer Michael Cohen could potentially implicate the President in campaign finance violations.

While Democrats are loudly seizing on the latest development as further evidence of corruption in Trump's inner circle, Republicans have largely taken a cautious approach as the leader of their own party faces the most serious controversy yet of his presidency.

In a New York court on Tuesday, Cohen entered a plea deal and said that "in coordination and at the direction of a candidate for federal office" he had kept information that would have been harmful to the candidate and the campaign from becoming public. The plea deal comes after a federal probe of payments by Cohen to help silence women who made claims of sexual encounters or affairs with Trump before the election. The women were not named in the plea, but two women have gone public this year with their allegations.

While Republicans acknowledge the gravity of Cohen's situation, they're not immediately criticizing the President for his alleged role.

Here's what top Republican lawmakers are saying:

House Speaker Paul Ryan

A spokesperson for Ryan said Tuesday night that the Wisconsin Republican was waiting for more information before weighing in.

"We are aware of Mr. Cohen's guilty plea to these serious charges. We will need more information than is currently available at this point," the spokesperson said.

Senate Majority Leader Mitch McConnell

McConnell, when asked by CNN about the Cohen news, declined to comment as he walked in a Capitol hallway Wednesday morning.

Sen. Orrin Hatch

Hatch, the most senior Republican in the Senate, told reporters Wednesday morning that the news constituted "serious charges" but did not go as far as to call the President's alleged involvement as high crimes or misdemeanors - the constitutional basis for impeachment.

"Well I'm not very happy about it," he said of the hush money. "It should never have happened to begin with."

Hatch, however, went on to say the "President should not be held responsible for the actions of the people he's trusted."

Senate Judiciary Chairman Chuck Grassley

Grassley brushed off Cohen's implication of the President as "speculation."

"All we know about it is he's plead guilty and everything else that you're asking me about is speculation," he told reporters. "And I don't think I should be speculating."

Sen. Bob Corker

Corker declined to weigh in on what legal jeopardy Cohen's plea could put Trump in, saying he didn't know enough and he wanted the legal system to play itself out.

"I can't imagine. I think anything the White House might do to interfere with Mueller at this point would end their presidency," Corker said, referring to the separate investigation let by special counsel Robert Mueller on potential collusion between Russia and Trump's campaign in the 2016 election.

Corker, a frequent Trump critic who is retiring at the end of his current term, also said he wasn't surprised by the revelations.

"I can't imagine people who are familiar with what's been going on in the White House are particularly surprised. But I realize the actual statement of yesterday makes it real. Personally, I'm not particularly surprised by what happened."

"I've been here 11.5 years, and I don't think I've witnessed anything like I've witnessed in the last year and a half," he continued. "Probably the American people haven't in modern times."