The race is on to see which congressional committee can land the first public appearance of James B. Comey, the ousted FBI director who has stayed out of the spotlight since President Trump fired him May 9.

Leaders of the Senate Intelligence Committee, operating the highest-profile investigation of Russian interference into the 2016 presidential campaign, are trying to reschedule a hearing with Comey after he declined their request to appear in private Tuesday.

On Wednesday, the Senate Judiciary Committee sent a formal request for Comey to come before the panel to discuss the FBI investigations into the Trump campaign’s ties to Russia and Hillary Clinton’s handling of classified material while secretary of state, and how those played into Comey’s dismissal.

Not to be outdone, Rep. Jason Chaffetz (R-Utah), the outgoing chairman of the House Oversight and Government Reform Committee, announced on Twitter that he had scheduled a hearing for Comey next week — before he had made contact with the former FBI director.

Who will go first? “That’s a very good question,” Sen. Susan Collins (R-Maine), a member of the Intelligence Committee, said Thursday.

Then Collins wondered whether the Justice Department’s appointment of Robert S. Mueller III to serve as the special counsel overseeing the criminal and counterintelligence investigation on Russia might prompt a request for all congressional committees to stand down.

That’s the one thing that brings unanimity from committee leaders, because every panel believes Comey should still testify. Each panel is operating under the auspices of conducting forthright oversight of a critical investigation, but lawmakers can barely hide their ambition at landing what would be a grand media spectacle.

It’s a lot like Barbara Walters and other TV personalities fighting over the first interview with a Hollywood starlet beset by scandal.

If you’re on the Intelligence Committee, you think Sens. Richard Burr (R-N.C.) and Mark R. Warner (Va.), the chairman and ranking Democrat of that panel, should decide the order of appearances by Comey.

“That sounds like a Burr-Warner responsibility — to figure out how to set a standard of which committee should get the first crack at these witnesses,” Sen. Roy Blunt (R-Mo.), a member of the intelligence panel, said Thursday.

Other committees think they have just as much a right at the first hearing.

“This is not exclusive. They have one part of this,” Sen. Dianne Feinstein (Calif.), ranking Democrat of the Judiciary Committee, said of the Intelligence Committee. She suggested her panel is a more traditional landing spot for Comey: “We are the oversight for the FBI.”

It’s understandable why Comey is in such demand. He is the man of the moment, whose allies leaked word that he kept meticulous memos of all his interactions with Trump. But he also has an unmistakable flare in his appearances that makes for great storytelling.

Trump mocked Comey as “a showboat” and a “grandstander” in an interview last week with NBC News, admitting that Comey’s handling of the “Russia thing” played a role in his dismissal. What Trump might see as a negative, however, lawmakers see as made-for-TV moments from which they get to reflect in the attention that he draws.

A native of Yonkers, north of New York City, the 6-foot-8-inch Comey has an authoritative voice and is a more appealing figure for daytime cable television than another five-person roundtable chewing on current events. He unwinds stories from the witness table with the timing and style of an Irish writer, slicing through moment-by-moment narrative.

[James B. Comey and the most riveting 20 minutes of congressional testimony]

His most famous appearance, as a civilian, came 10 years ago this week, when the Senate Judiciary Committee was conducting an investigation into the Bush White House’s dismissal of U.S. attorneys in 2005. Comey had been deputy attorney general in 2003 and 2004, overseeing those federal prosecutors, but that day he unfurled a story only indirectly related to the inquiry at hand: the moment in 2004 he rushed to the hospital bedside of John Ashcroft, the attorney general, to prevent President George W. Bush’s top advisers from getting Ashcroft to overrule his deputy’s decision on a surveillance program.

Asked a key question at the hearing, he paused for six seconds and stammered for another 10 seconds, before finally saying: “I’ve actually thought quite a bit over the last three years about how I would answer that question if it was ever asked, because I assumed that at some point I would have to testify about it.”

He then delivered a spellbinding account, punctuated by the first public admission that he and Mueller, then the FBI director, were willing to lead a mass resignation of Justice and FBI officials if they were overruled.

After succeeding Mueller as FBI director, Comey continued to command the hearing rooms on Capitol Hill. On March 20, appearing before the House Intelligence Committee, Comey explained that the Justice Department and FBI never acknowledge a criminal investigation is happening unless “it is in the public interest.”

He then delivered the gut punch that would be played over and over again, confirming the investigation into any links from the Trump campaign to Russian operatives and pausing at just the right moment for effect.

“This is one of those circumstances,” Comey said. “I have been authorized by the Department of Justice to confirm [pause] that the FBI, as part of our counterintelligence mission, is investigating [pause] the Russian government’s efforts to interfere in the 2016 presidential election.”

That’s why congressional committees are jostling to get the first crack at Comey.

Collins said that she believes that, even if Mueller wants to wall him off as a fact witness in his investigation, Comey should at least be permitted to come testify about the memo he wrote about a mid-February meeting with Trump in which the president appeared to ask him to drop an investigation into former national security adviser Michael Flynn.

First reported by the New York Times and confirmed by The Washington Post and other outlets, that memo is out in the public, Collins said, and his discussion of it “would not tip off a witness.”

With so much demand, for Comey and other witnesses in the multiplying investigations, House Speaker Paul D. Ryan (R-Wis.) was pressed on whether he would referee the disputes.

“I’ll leave it up to the committees to determine that,” he said.

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