"We want to see what develops, but at this point, I have not seen anything that is that alarming," Rep. Robert Aderholt (R-AL), who said a lot of the reports simply involve "speculation."
"It is very clear that a lot of people want to see the President distracted," Aderholt added to reporters gathered outside the offices of the Republican National Committee.
"At the end of the day, the President has his job to do - we have our job to do - but it's important to get all the facts straight," said Rep. Markwayne Mullin (R-OK).
But there were some voices in the GOP who saw the need to do more.
"It's very important however that Director Comey come before the Congress as soon as possible," said Rep. Leonard Lance (R-NJ).
Some Republicans said the focus on the President was all wrong, echoing White House calls for an investigation of leaks about the Russia matter and Flynn.
"That's really what the story ought to be, not something the President said to somebody in a private meeting," said Rep. Barry Loudermilk (R-GA), who said he wants Comey questioned about that.
"I think he needs to come up here and we need to find out where a lot of these leaks are coming from," Loudermilk added.
Others questioned the veracity of any notes taken by the former FBI Director, and whether the Congress should even pay attention to such evidence.
"He could have done the notes two days ago," said Sen. Jim Inhofe (R-OK).
As for the President, he was out of town, giving the commencement address at the U.S. Coast Guard Academy in Connecticut - in that speech, he knocked the press for giving him historically bad treatment.
"Look at the way I've been treated lately, especially by the media; no politician in history - and I say this with great surety - has been treated worse or more unfairly," Mr. Trump said.
As for the investigation on Capitol Hill, the Senate Intelligence Committee on Wednesday sent a letter to Comey, as well as the current Acting FBI Director, Andrew McCabe, asking Comey to return for testimony, and to get any relevant notes and memos about contacts with the President.
Also asking for the Comey memos was the Senate Judiciary Committee, which asked for Comey memos to be handed over within one week.
"This is all about finding out as many facts as we can," said Sen. Marco Rubio (R-FL), as he was trailed by a pack of reporters while walking to the Senate floor for a vote.
"I think we need to be privy to facts," Rubio said.