Perhaps most important for Republicans judging Paul's 2016 viability and his potential to turn enthusiastic fans at rallies into GOP votes at the polls is this: At a time when Americans despise the notion of more foreign entanglements, he has somehow made President Obama and his Democrats look like interventionist hawks. "The thing that could transform our country and transform the youth vote and transform a lot of votes would be if, all of a sudden, the Democrats become the party of war. I think they really essentially are now," Paul said in an interview. Young people "fight all the wars," he said, and might look to the GOP "if there were a Republican Party that were more reluctant to go to war."

This is not to say Paul is a perfect candidate in the eyes of young, minority, and female Americans—far from it. He is firmly opposed to abortion and has introduced a bill giving fertilized eggs the same rights as people. He backs drilling for oil in the Arctic National Wildlife Refuge. And he has an exceedingly cramped view of what the government should be doing. A proposal he released this year to balance the budget in five years would eliminate the Commerce, Education, Energy, and Housing and Urban Development departments; turn Medicaid and food stamps into block grants; add private options to Medicare and Social Security; and repeal the Affordable Care Act.

That minimalist theory of government would be a hard sell even to voters who tell pollsters they think government is doing too much. Asked if there's anything the government should mandate, for example, Paul said, "The government should prevent violence .… They should enforce contracts. They should prevent fraud. But I don't think the government ought to mandate behavior outside of violence."

What does that mean in practice? Nothing that would appeal to liberals or even moderates, as Paul is aware. He told the medical students, "There's a philosophic debate which often gets me in trouble," then waded into it anyway, saying he doesn't believe health care is a right. "I think we as physicians have an obligation, as Christians we have an obligation, to our fellow man. I really believe that, and it's a deeply held belief," he said. "But I don't think you have a right to my labor. You don't have a right to anybody else's labor. I mean, food's pretty important. Do you have a right to food, water? As humans, yes, we have an obligation to give people water, to give people food, to give people health care. But it's not a right."

It's a classic libertarian view, delivered by a short, unassuming guy in khakis and scuffed boots. And, by all appearances, it's an honest reflection of what he believes in and would pursue if he were in the White House. If he were commander in chief, sworn to protect the nation, he said, he'd be willing to live by the restrictions he wants to impose on other presidents. "It's everything that I stand for," Paul said with a disarming straightforwardness that is as much a part of his presentation as his jokes.