But Paul said he was happy with his passionate base, saying he believed it would propel him into the thick of the Republican race.

"We don't have to immediately convince 51 percent of the voters," Paul said. "You do need a hardcore group of people who understand, volunteer and work hard. Once you get to 10 percent, you have the number … We very well could be, and most likely are, on the verge of an explosion."

Much of the evening focused on issues like the war, drug policy and political freedoms — topics of common ground between Paul and Stewart's mostly young, liberal audience.

"I hate the war on drugs a lot more than I fear drugs themselves, and I hate drugs," Paul said.

But Stewart and Paul also sparred on substantial critiques of libertarian versus liberal political philosophy. Stewart pressed Paul on why voters should embrace his vision for the country, when environmental and labor abuses occurred during the laissez-faire period of limited government during the Industrial Revolution.

"It's been tried, but it's never been perfect, but has socialism or authoritarianism been perfect? No, it's been horrible," Paul said.