Scruggs, a wealthy Mississippi trial lawyer, is looking to overturn his 2009 conviction for trying to influence a judge by suggesting that he would float the judge's name to Lott for a federal judgeship. Lott has admitted to talking with the judge, Bobby DeLaughter, but Lott himself was never charged with any wrongdoing.

Influencing judges is known as "honest-services fraud" because the act denies other parties of the honest services to which they are normally entitled.

According to the Tennessee publication The Commercial Appeal, lawyers for Scruggs aim to overturn his conviction by leaning on a 2010 Supreme Court ruling that says honest-services fraud must involve bribes or kickbacks. Scruggs is making the case that he only offered an endorsement, which is not a financial payment.

As they make their case, Scruggs's lawyers want to interview the two Senate staffers, possibly as early as next week.

On Wednesday, Reid said the testimony will involve the "brief phone call" between Lott and Judge DeLaughter.

"Both Senators Lott and Cochran would like to assist by providing relevant evidence from their staff in this proceeding," Reid said in comments inserted into the Congressional Record, but that do not appear to have been spoken on the floor. "This resolution would accordingly authorize Senator Lott's and Cochran's employees, and any other Senate employee from whom evidence may be necessary, to provide evidence in this action, with representation by the Senate Legal Counsel."

Reid also defended Lott by saying "Neither Sen. Lott nor anyone on his staff was aware of the defendant's scheme."

— This story was updated at 2:39 p.m. to reflect that passage of the resolution and remarks on it appear to have been inserted into the Congressional Record.