"The fact is that a four-page summary cannot possibly illuminate what this thorough of an investigation uncovered. I find it so disappointing that so many are rushing to judgement without being able to see the full report or all of the underlying facts," Feinstein said from the Senate floor.

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"I have consistently supported the proposition that his report ought to be released to the greatest extent possible, consistent with the law. … I think we should be consistent in letting the special counsel actually finish his work and not just when we think it may be politically advantageous to one side or the other," McConnell added.

Under Senate rules any one senator can try to pass a bill or resolution by unanimous consent. But the move requires every other senator to sign off, meaning one member can also block their request on the floor.

It's the third time Democrats have tried to pass the House resolution, which argues there is “overwhelming public interest” in the government releasing the contents of the high-profile report. The resolution calls on the Justice Department to fully release the report to Congress and to release it to the public “except to the extent the public disclosure of any portion thereof is expressly prohibited by law.”

McConnell's move has been backed up by some GOP senators. Sen.(R-Fla.) defended him on Monday, saying the Mueller resolution was the "an unnecessary solution looking for a problem."