WASHINGTON -- Pressure continues to mount on former national security adviser Michael Flynn to testify before Congress about possible connections between the Trump campaign and Russia even without protection from prosecution, CBS News correspondent Errol Barnett reports.

Flynn was fired from the White House in February for lying to Vice President Mike Pence about his contacts with the Russian ambassador.

Flynn’s lawyer released a statement Thursday saying his client “has a story to tell,” but wants protection in order to tell congressional intelligence committees and the FBI what he knows. And that has all of Washington wondering what exactly that could be.

Even some Republicans like Rep. Jason Chaffetz of Utah, the chairman of the House Oversight Committee, are puzzled by Flynn’s request for protection from prosecution.

“Well, it doesn’t look good,” Chaffetz told Fox News on Friday. “I don’t know -- the witch hunt, I don’t buy that either. We’re just trying to get to the facts.”

Rep. Adam Schiff, the top Democrat on the House Intelligence Committee, called Flynn’s immunity request “a grave and momentous step.”

Schiff went to the White House Friday to review the intelligence previously provided to Republican committee chairman Rep. Devin Nunes, who is facing questions about possible coordination with White House officials. Schiff called for the documents to be shared with the full intelligence committees.

On Friday, Mr. Trump refused to answer questions at the White House when CBS News chief White House correspondent Major Garrett asked about Flynn’s request. But Mr. Trump earlier encouraged Flynn to ask for immunity, tweeting that the ongoing congressional inquiries are nothing short of a “witch hunt.”

Press secretary Sean Spicer said Mr. Trump is supportive of Flynn testifying, but dodged questions about whether the president is trying to influence the investigations.

“He could have just said ‘testify,’” Garrett said during Friday’s press briefing. “He said he should get immunity.”

“The president is very clear that he wants Mike Flynn to go and be completely open and transparent with the committee and whatever it takes to do that he is supportive of,” Spicer replied.

Even if Flynn is granted congressional immunity, he could still face prosecution by the Justice Department.

During the presidential campaign, both Flynn and Mr. Trump said potential immunity for rival Hillary Clinton’s associates was tantamount to an admission of guilt.

“When you are given immunity that means you’ve probably committed a crime,” Flynn said on NBC’s “Meet the Press” in September.

“If you’re not guilty of a crime, what do you need immunity for?” Mr. Trump said at a rally the next day.