(CNN) Senate Republicans and Democrats are split over whether they can tell the press and public what they learn from deputy Attorney General Rod Rosenstein at a highly-anticipated briefing Thursday afternoon on how and why former FBI Director James Comey and was fired .

Republicans insist the briefing, which will be held in a secure room known as a Sensitive Compartmented Information Facility, or SCIFF, will be classified and therefore anything senators learn in it must be kept secret.

That is upsetting Democrats, who demanded the briefing after Comey's surprise firing by President Donald Trump last week, and who say they want -- and intend -- to inform the public about the non-classified parts of what they hear.

"Frankly, in terms of it being a briefing that can restore public confidence in the process that led to the firing of the FBI director, if we are literally unable to make any comment about anything, it won't be a very useful briefing," Democratic Sen. Chris Coons of Delaware told CNN Wednesday.

Senators are generally highly aware of what they are allowed to say when leaving a sensitive briefing like this. Disclosure of classified information is against the law and many senators are wary to talk to reporters when for fear they will accidentally reveal secrets. Other senators, especially those who deal regularly with classified national security information, are more comfortable and will discuss non-classified information with the press, something that helps them shape the narrative of a given issue.

Democratic Sen. Richard Blumenthal of Connecticut wants to press Rosenstein about memos Comey wrote detailing his private conversations with Trump, including Comey's damaging assertion that Trump asked him not to pursue a criminal investigation of his just-fired national security adviser, retired Gen. Michael Flynn.

Blumenthal huddled in a strategy session with other Democrats Wednesday to get ready for Rosenstein's briefing. As he was leaving, he dismissed the insistence by Republicans he wouldn't be able to talk to reporters or his constituents about what he learned in the session.

"The briefing is classified only to the extent that specific information is classified," Blumenthal said. "You can't classify all the answers just by having it in the SCIFF."

The senators spoke before Rosenstein announced he had appointed former FBI Director Robert Mueller as a special counsel to investigate Russia's alleged interference in the US election. The decision resolves a key issue for Democrats who have pushed for an independent investigation and will likely ease tensions in the briefing, although senators still say they have a lot they want to learn from Rosenstein.

Dozens of reporters, network camera crews and photographers, will gather outside the entrance to the SCIFF in the basement of the Capitol ahead of the 2:30 p.m. briefing and will press senators for any bits of information when they depart.

"I think anytime we have a discussion in the SCIFF it's normally classified," said Sen. John Thune of South Dakota, the third-ranking Senate Republican, explaining the GOP's position. "That's the reason it's down there. So we can get a presentation form the appropriate personnel in the administration about information that's highly sensitive and classified."

The Democratic senators said they expect Rosenstein to slip back and forth between material that is classified and will tell the senators what is off-limits for the public and what is okay to reveal.

But Thune said Senate Majority Leader Mitch McConnell, R-Kentucky, and Senate Minority Leader Chuck Schumer, D-New York, who will run the briefing, would have to reach an agreement about what can be talked about publicly.

"That determination needs to be made by our two leaders and, obviously, by the Justice Department," Thune said. "I assume Mr. Rosenstein would have a lot of input as to what exactly is subject to classification rules and what is not. I would be surprised if there were a lot coming out of that discussion tomorrow that Democrats would feel comfortable coming out and talking about. But we'll see."

The SCIFF is expected to be set up like an auditorium with a table up front for Rosenstein and then rows and rows of chairs for the senators. There will be a microphone for senators to ask questions. The order of questions will be based on the order of senators' arrival, which will be noted by a staff member.

"I think we have to make it clear up front how much of the deputy Attorney General's testimony to the all-senators briefing tomorrow is genuinely classified and sensitive and how much of it is routine business of the Department of Justice that can be talked about afterwards," Coons said. "I'm fairly certain that a broad range of the things we will be asking tomorrow can be answered and those answers can be shared publicly. But we have to be sensitive that there is an ongoing FBI counter-intelligence investigation and there are classified aspects that could be asked about."

"If there is a discussion of sources and methods of collecting intelligence, that sort of things, those are things we don't want to disclose and that's one of the issues we're talking about," Thune said. "What the President said when the Russians were here."