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Asked if he would vote against a resolution that didn't include calling the whistleblower, Paul said that he would.

The senator's comments come as he's made waves this week, calling for the identity of the whistleblower, who is at the center of the House impeachment inquiry, to be publicly disclosed.

Trump and some of his allies are also adopting this approach to combat the impeachment proceedings, calling for the whistleblower's name to become public. The president and his supporters argue that it would allow the president to confront his accuser and help disclose any potential biases or political motivations of the individual.

Paul, during a Monday rally with Trump in Kentucky, called on the media to publish the name of the whistleblower. The next day he told reporters that he "probably will" disclose the name.

"I think it's so partisan ... that I don't know how we get together on rules," Paul said about the chances for a deal, but added that he would "cooperate" if senators were allowed to make motions and both sides were able to call witnesses.