A live microphone on Wednesday caught Senate Minority Leader Mitch McConnell (R-Ky.) and Sen. Rand Paul (R-Ky.) discussing the GOP's shutdown strategy.

Both suggested Democrats would be hurt by their refusal to negotiate with Republicans over ending the shutdown.

“I know we don’t want to be here, but we’re going to win this, I think," Paul said at one point in the conversation.

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A video of the two was posted on conservative website, mofopolitics.com. Both senators did not appear to realize they were being recorded.

"I just go over and over again; we’re willing to compromise; we’re willing to negotiate,” Paul said softly into McConnell’s ear.

“I don’t think they poll-tested we won’t negotiate. I think it’s awful for them to say that over and over again,” Paul added.

“Yeah, I do, too,” said McConnell, who had just returned from a White House meeting with President Obama and other congressional leaders on the shutdown.

“And I just came back from the two-hour meeting with him, and that was basically the same view privately as it was publicly,” McConnell said.

Paul seemed to suggest that if Republicans highlight that they've moved on from defunding the healthcare law to delaying it, they could win the public relations fight on the shutdown.

“I think if we keep saying we wanted to defund it, we fought for that, but now we’re willing to compromise on this …,” Paul said.

The White House and Senate Democrats have said they would not accept measures delaying or defunding ObamaCare in connection with funding the government or raising the debt ceiling. They have also objected to narrower measures, such as a repeal of a tax on medical devices meant to pay for a portion of the health law.