In a conversation picked up by a hot mic Wednesday, Sen. Rand Paul and Senate Minority Leader Mitch McConnell were heard discussing the talking points Republicans have employed during the government shutdown standoff.

"I just did CNN and I just go over and over again, 'We're willing to compromise. We're willing to negotiate.' I think... 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 said in the candid conversation captured by local Kentucky news station WPSD 6.

McConnell agreed with Paul's assessment: "Yeah, I do too and I, and I just came back from that two-hour meeting with them and that, and that was basically the same view privately as it was publicly."

Paul added, "I think if we keep saying, 'We wanted to defund it. We fought for that but now we're willing to compromise on this,' I think they can't, we're gonna, I think... well, I know we don't want to be here, but we're gonna win this, I think."

Paul has spent the past week positioning himself as a voice of reason in the GOP, calling on his colleagues to pass a continuing resolution that would not tie government funding to changes to Obamacare, and hosting a bipartisan chat over coffee on the steps of the Capitol.

His conversation with McConnell makes clear that he thinks his party will only "win" the shutdown fight if they are seen by the public as eager to negotiate.

But it's unclear whether they believe they can actually hash out a deal. At the beginning of the conversation, Paul told McConnell, "I just didn't see an end."

Paul's office, much of which has been furloughed, did not immediately respond to BuzzFeed's request for comment.

UPDATE: Reached for comment, an aide e-mailed this statement by Paul: "Everything that was said 'in private' was also said just minutes earlier in front of cameras during a CNN and a Fox interview."

CORRECTION: Paul is talking about the Democrats' reluctance to negotiate in the clip. (10/3/13)