Washington (CNN) An independent counsel's investigation very nearly brought down a Democratic president nearly 20 years ago. Bear that in mind when reading the news that the top Senate Democrat is calling to potentially reinstate the lapsed office under which Republicans launched the Whitewater investigation.

Special prosecutors have a track record of looking for one thing and finding something else. Ken Starr went looking at Bill and Hillary Clinton's land deals and he ended up with Monica Lewinsky and a President who lied under oath and was found in contempt of court.

Former President Clinton on the day Republican House majority adopted a motion to launch an impeachment inquiry into his presidency.

You know Attorney General Jeff Sessions is facing some real political trouble because even Republicans were calling on him to recuse himself. Sessions did, by the way, in an afternoon press conference.

Rep. Jason Chaffetz was the first Republican out of the gate Thursday morning, when he tweeted, "AG Sessions should clarify his testimony and recuse himself."

That was perhaps smart politics by Chaffetz, putting him on the record about Sessions and setting a tone of accountability. It should be noted, however, that Chaffetz is one of the few Republicans who has the power to launch an investigation into the attorney general's activity.

But Chaffetz won't be launching any such investigation; House Republicans are relying on their intelligence committee to do that. Democrats have taken note -- they repeatedly point out Chaffetz's committee was more than happy to investigate Democrat Hillary Clinton on both her email server and the Benghazi terror attack.

Calls for Sessions' recusal also raise another interesting question -- recuse himself from what?

There is an active FBI investigation -- and the FBI director reports to the attorney general -- but little has been said publicly about it.

At least one Republican, Sen. Lindsey Graham, wasn't completely sure Thursday morning the FBI was investigating anything. Graham met with FBI Director James Comey Thursday afternoon to get some answers.

"I just want to know what's going on," Graham said before the meeting. "I don't want to know the details of the investigation. If there is not one, I want to know it. If there is one, I want to know it and the rest of us need to stay out of it if there is."

The South Carolina Republican, who along with Sen. John McCain is known for taking a hard line against Moscow, said Wednesday night at a CNN town hall that Trump has a "blind spot" when it comes to Russia, has launched one of the handful of congressional inquiries regarding Russia.

But Graham's subcommittee is just looking at Russian efforts to meddle in the election.

The House and Senate Intelligence Committees are conducting the main congressional investigations, looking concurrently at both potential contacts between political campaigns and the Russians, and at the leaks that brought contacts to light.

Their investigation depends very much on the FBI -- which is controlled by Comey, who works for Sessions.

"We know less than a fraction of what the FBI does," said Rep. Adam Schiff, top Democrat on the House Intelligence Committee, after a briefing Thursday. He said the FBI had refused to answer some of lawmakers' questions on the matter. Committee Chairman, GOP Rep. Devin Nunes, disputed Schiff's assessment.

Still, the intelligence committees are the appropriate place for Congress to act, according to House Speaker Paul Ryan, who also called on Sessions to recuse himself Thursday morning. The intelligence committees, Ryan said, are best equipped to investigate these sensitive issues without compromising US intelligence.

"The intelligence committee, just so you know, they've been doing an investigation for some time now. They just recently added more scope to that investigation on a bipartisan basis," he said.

Those congressional inquiries aren't good enough for Senate Minority Leader Chuck Schumer, who had three demands regarding Sessions during his own news conference Thursday.

JUST WATCHED Schumer calls on Sessions to resign Replay More Videos ... MUST WATCH Schumer calls on Sessions to resign 01:50

First, he called on the Justice Department to appoint an independent special prosecutor to look into ties between the Trump campaign and White House. Barring that, or if Schumer doesn't think the potential special prosecutor is independent, he wants to work with Republicans to revive the independent counsel law.

And finally, he specifically wants Sessions investigated.

Each of those will require cooperation from the GOP, who don't seem likely to agree.

"We don't even have the law," Ryan said, when asked about a special prosecutor.

JUST WATCHED Ryan: No evidence yet of collusion Replay More Videos ... MUST WATCH Ryan: No evidence yet of collusion 01:21

Others, like Graham, are more open to the idea. He said if the FBI uncovers any sort of wrongdoing with regard to the Trump campaign and Russia, a special prosecutor would be warranted. Graham -- who became a national figure for his role in the Clinton impeachment drama -- was not asked about reviving the office of independent counsel.

"If there is something there," he said, "and it goes up the chain of investigation, it is clear to me that Jeff Sessions, who is my dear friend, cannot make this decision about Trump."

JUST WATCHED Graham, McCain weigh in on Sessions report Replay More Videos ... MUST WATCH Graham, McCain weigh in on Sessions report 03:00

McCain said the Senate Armed Services Committee, which he chairs, would look at "certain military aspects" of the Russia affair, but he said the intelligence committees should be given a chance to do their work before any other special investigation is enacted.

"I'd like to give them a chance to examine the facts and come up with some conclusions before I leap to the need for a whole new special committee. When you set up a special committee, there has to be -- it's a long process," he said during the CNN town hall.