Graham, a close ally of President Trump's, has outlined several areas he wants to probe now that he has the Judiciary Committee gavel.
They include the FBI's handling of its investigation into Hillary Clinton's private email server and the Foreign Intelligence Surveillance Act (FISA) warrant applications targeting former Trump campaign aide Carter Page.
"This is going to be like the History Channel it turns out. Instead of taking a look at the current issues, Lindsey Graham wants to go back and answer important questions about the Bermuda Triangle and Hillary Clinton," Durbin told The Hill.
Sen. Sheldon Whitehouse (D-R.I.), another member of the panel, said maybe Graham should "investigate Benghazi some more too" - an apparent reference to a years-long House probe that Democrats considered a political stunt.
Graham's plans come while tensions on the panel linger from the deeply partisan fight over Supreme Court Justice Brett Kavanaugh's confirmation.
Graham won praise from conservatives during that battle, when he exploded at Democrats during the hearing and accused them of trying to "destroy this guy's life" after sexual assault allegations surfaced against Kavanaugh.
He has cut deals with Democrats on the Judiciary Committee, including helping to draft legislation with Sens. Christopher Coons (D-Del.), Cory Booker (D-N.J.) and Thom Tillis (R-N.C.) that would protect special counsel Robert Mueller from being fired without "good cause." The White House and Majority Leader Mitch McConnell (R-Ky.) oppose that bill.
Coons, a member of the Judiciary Committee, encouraged Graham to thread the needle carefully, adding that "it depends how divisive partisan topics are approached."
Democrats are now pushing for the committee to dig into an explosive BuzzFeed News report that former Trump lawyer Michael Cohen told Mueller that Trump personally directed him to lie after his election about the timing of when the negotiations involving a Trump Tower project in Moscow ended in an effort to obscure the president's involvement.
"Our committee must conduct a thorough investigation of the President's involvement in these crimes and whether he obstructed justice to hide them. ... The hour to put country before petty partisan differences has come," he added.
Graham has aligned himself closely to Trump on some key areas within the panel's jurisdiction.
Graham told reporters earlier this month that he would do a "deep dive into the FISA issue" as chairman of the Judiciary Committee. And he told Fox News last month that he believed the FBI "phoned in" the Clinton probe and were "in the tank" for the Democratic presidential nominee.
Graham also
said late last year that he would "totally" investigate the FBI's handling of its investigations into Russian interference in the 2016 presidential election and Clinton's email. He added separately last month that he would "get to the bottom of" the FISA warrant applications against Page and that he wanted to have "an in-depth discussion" with former FBI Director James Comey.
Graham described as "stunning" a Fox News report that Justice Department official Bruce Ohr discussed his views on a controversial research opposition dossier on Trump with individuals now on special counsel Robert Mueller's probe.
Graham's investigations could overlap with work by the Senate Intelligence Committee, which is deep into its own probe of the 2016 election. The two panels previously bumped elbows under Sen. Chuck Grassley (R-Iowa), with both demanding to hear from Comey and meet with Mueller.
"The Senate Judiciary Committee has oversight responsibility for the DOJ and the FBI and so I think oversight hearings ... could be useful," he said.