McCain introduced a resolution Tuesday expressing the Senate's support for Holder to appoint a special prosecutor. But Sen. Ron WydenRonald (Ron) Lee WydenWATCH: Dems say Trump will look like he has something to hide if he avoids Muller interview House funding bill includes bipartisan Medicare reforms Trump approves Indiana Medicaid work requirements MORE (D-Ore.) objected after McCain asked for unanimous consent that the Senate proceed to consideration of his resolution.

"What is at issue here is whether or not we are going to give an opportunity for U.S. attorneys, professionals in their fields, to handle this particular inquiry," Wyden said. "And I see no evidence, Mr. President, that the way U.S. attorneys are handling this investigation at this time is not with the highest standards of professionalism."

McCain said that recent military and intelligence leaks warranted outside legal counsel to investigate the leaks.

"The damage to our national security has been articulated by many both in and outside the administration," McCain said.

A week earlier, McCain had called for a special counsel to look into a number of leaks related to a report about an Obama administration "kill list" of terrorists as well as a story about a U.S. cyberattack against Iran. Democrats have so far refused to back McCain on the resolution.

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"So, here we are with a very serious breach of national security, in the view of some the most serious breach in recent history, and it clearly cries out for the appointment of a special counsel," McCain said during a colloquy on the Senate floor with Sen. Lindsey GrahamLindsey Olin GrahamMcConnell: 'Whoever gets to 60 wins' on immigration Overnight Tech: Uber exec says 'no justification' for covering up hack | Apple considers battery rebates | Regulators talk bitcoin | SpaceX launches world's most powerful rocket Overnight Cybersecurity: Tillerson proposes new cyber bureau at State | Senate bill would clarify cross-border data rules | Uber exec says 'no justification' for covering up breach MORE (R-S.C.). "I would remind my colleagues, and my friend from South Carolina will remind our colleagues, that when the Valerie Plame investigation was going on my colleagues on the other side of the aisle argued strenuously for the appointment of special counsel at that time."

Specifically, the resolution would require Holder to "delegate to an outside special counsel all of the authority of the Attorney General with respect to investigations by the Department of Justice of any and all unauthorized disclosures of classified and highly sensitive information related to various United States military and intelligence plans, programs, and operations reported in recent publications."

The resolution would have given the counsel authority to investigate the leaks independent of the Justice Department. It also required the counsel to assess how much of the damage of the leaks could be repaired.