Sen. Lindsey Graham, R-S.C., speaks with reporters on Capitol Hill in Washington, March 16, 2022.
CNN  — 

The Georgia prosecutor leading an investigation into efforts by former President Donald Trump and his allies to overturn the 2020 election urged the Supreme Court on Thursday to clear the way for the testimony of Republican Sen. Lindsey Graham.

“The Fulton County Special Purpose Grand Jury seeks to question Senator Lindsey Graham regarding certain activities related to its ongoing investigation into possible criminal activity surrounding the 2020 general elections in Georgia,” Fulton County District Attorney Fani Willis wrote in the new filing.

She stressed that Graham’s efforts to postpone his testimony would be “unavoidably harmful to the administration of the grand jury investigation” and would “harm the public’s interest in the timely and effective resolution” of it.

The filing came in response to the South Carolina senator’s emergency request last week asking the justices to halt the testimony while the legal challenges play out. Graham has argued that he should not have to abide by the subpoena because his testimony is foreclosed by the Constitution’s Speech or Debate clause, which shields lawmakers from certain law enforcement action for conduct connected to their legislative duties.

If Graham prevails, critics fear that it will embolden other members of Congress to make similar claims in an attempt to shield speech that falls outside the protections of the Speech or Debate Clause. The clause reads that “for any Speech or Debate in either house” members of Congress “shall not be questioned in any other place.”

Willis has indicated that she would like to question Graham on calls he made to election officials in Georgia after the 2020 election. Lawyers for the senator characterize the calls as “investigatory phone calls” carried out in furtherance of a legitimate legislative activity meant to inform him on his upcoming certification decision.

On Monday, Justice Clarence Thomas, who supervises the lower courts involved in the case, temporarily blocked the testimony. Thomas’ move was an administrative stay that was most likely issued to give the Supreme Court justices more time to consider the dispute. Thomas’ order also signaled that he would ultimately vote in the case. His critics believe he should recuse himself from matters concerning the last election because of his wife, Virginia “Ginni” Thomas’ political activities.

In the new filing, Willis argued that individuals who were on the calls have publicly indicated their understanding that Graham was suggesting or impl