In a free-flowing conversation, Paul was pessimistic about both the direction of his party and the country.
Asked about the future of the GOP, Paul said: "I think of it in terms of the country and the future of the Republican and Democratic party, and there's not much good in either party at the rate we're going, and right now I think in the near future the Republican Party has a long way to go to build their credibility up again."
Paul was similarly downbeat about the Democratic leadership.
"The Democrats aren't doing any better than the Republicans," said Paul. "I mean they're spending more, they're printing more and they're doing exactly the wrong thing as well, so eventually they're going to get blamed."
Watch Paul discuss the future of the Republican party below:
Paul also said he gets asked frequently about raising money through online donations. The key to his fundraising success, he suggested, was his message more than his campaign's technological prowess.
He downplayed his past as a cyber sensation.
"I don't know how to raise money on the Internet," Paul said. "The question that should be asked is why are they motivated, why are they interested, and the answer is they like the message and they know this system isn't working."
Paul also noted that he had skipped President Obama's speech to a joint session of Congress on Tuesday. He pointed out that he hadn't gone to President George W. Bush's State of the Union addresses, either. Paul said it was "unbearable" to go to those speeches and see people "yelling and cheering about what we were not doing."
Asked by Schiffer he will make another run for the presidency, Paul wouldn't rule it out entirely. But he downplayed the possibility.
"Probably not, it's not on my agenda," said Paul.
Watch Paul discuss the troop increase in Afghanistan below:
Check back this afternoon at CBSNews.com/washingtonunplugged for our regular show with guests Newt Gingrinch and author Craig Mullaney.
There will also be a roundtable with CBS News Political Director Steve Chaggaris and Washington Post White House reporter Michael Fletcher, who will discuss President Obama's speech to Congress and the national budget.