(CNN) There is an active debate in the halls of the United States Senate about whether to release the FBI background report about President Donald Trump's Supreme Court nominee Brett Kavanaugh, a document that as of Tuesday evening has yet to arrive on Capitol Hill.

Several Republicans are pushing for public release because they have become convinced it will be exculpatory or, more cynically, they expect it to leak to the public anyway -- and it's safer to have the full thing in view, not just cherry-picked parts that boost one side or another.

But that feeling does not include all Republicans. Senate Majority Leader Mitch McConnell indicated on Tuesday afternoon that the report or findings of the FBI's investigation into Kavanaugh would not be made public.

"We will get an FBI report soon," the Kentucky Republican told reporters during a weekly news conference. "It will be made available to each senator, and only senators will be allowed to look at it. That's the way these reports are always handled."

Sen. John Cornyn of Texas, the second-ranking Republican senator and a member of the Judiciary Committee, told CNN he does want the FBI to say something publicly.

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