Graham says he 'totally' will investigate the FBI's handling of Russia and Clinton probes

"Totally," the South Carolina Republican told CNN when asked if he would look into the FBI's handling of those probes. "The oversight function will be very much front and center."

Graham has been a longtime critic of the FBI's handling of those investigations -- and has called for a second special counsel to investigate what happened. And if Iowa Republican Sen. Chuck Grassley steps aside from running the Senate Judiciary Committee to chair the Senate Finance Committee, as is widely expected, Graham would be poised to run the powerful panel that oversees the FBI. Graham's comments are the latest sign that the Senate GOP will be a counterbalance of sorts to House Democrats, who plan to end the House Republican probe into the FBI and launch a flurry of new investigations in their new majority next year.

Graham also said Tuesday that he would support Senate passage of a bill to protect special counsels like Robert Mueller from political pressure, even though he said, "I don't see any threat to Mueller." Democrats have demanded quick passage of that bill after President Donald Trump fired Jeff Sessions as attorney general last week and named Mueller critic Matt Whitaker to the post as acting AG.

"I'd support it if it came to the floor, but I don't see any threat to Mueller," said Graham, who cosponsored the special counsel bill that the Senate Judiciary Committee approved this year. "The idea of a check and balance going forward makes sense to me. ... I don't see an imminent threat to Mueller, but I've always been supportive of the idea."

Republican leaders have rejected moving on that measure, even as Democrats have demanded that it be added to a must-pass spending bill to keep the government open past early December.

But Graham, who spoke with Whitaker last week, said he's convinced that the new acting attorney general won't interfere with the Mueller probe.

"He understands the position he's in," Graham said. "He's probably not going to be the next attorney general, but this is a chance for him to show he can handle responsibility. This enhances his political future if he handles this well. It would be a nightmare for us to truncate the Mueller investigation."