Asked by Ms. Maddow if a private business had the right to refuse to serve black people, Mr. Paul replied, “Yes.”

Image Republican U.S. Senate candidate Rand Paul at his campaign headquarters on Wednesday. Credit... Ed Reinke/Associated Press

“I’m not in favor of any discrimination of any form,” Mr. Paul continued. “I would never belong to any club that excluded anybody for race. We still do have private clubs in America that can discriminate based on race. But I think what’s important about this debate is not written into any specific ‘gotcha’ on this, but asking the question: what about freedom of speech? Should we limit speech from people we find abhorrent? Should we limit racists from speaking?”

“I don’t want to be associated with those people,” he said, “but I also don’t want to limit their speech in any way in the sense that we tolerate boorish and uncivilized behavior because that’s one of the things freedom requires is that we allow people to be boorish and uncivilized, but that doesn’t mean we approve of it.”

While those views reflect the libertarian philosophy that Mr. Paul and many Tea Party members have embraced, they are politically treacherous for someone making an appeal to the electorate at large, as Mr. Paul learned as he struggled with questions about whether he thought the government had a role in regulating food safety and working conditions.

Congressional Republicans were peppered with questions about Mr. Paul’s position on civil rights. “I just want to be on the record that I believe the Interstate Commerce Clause was properly used by the courts and the Congress to make sure that when you travel in this country you can’t be denied food and lodging based on your race,” Senator Lindsey Graham, Republican of South Carolina, said. “That is not a big heavy lift for me.”

Mr. Paul’s father, Representative Ron Paul, a Texas Republican who ran for president in 2008, angrily defended his son, saying he was being treated unfairly. “I think there’s a lot of resentment because he became a star,” said Mr. Paul, who ran for president in 2008.

Democratic leaders have long said that they viewed Mr. Paul as the weaker of the two major candidates in the Republican primary — the other was Trey Grayson, the secretary of state — because, they said, his views would not be embraced by the general electorate as they were by primary voters. That view was shared by many establishment Republicans, as reflected by the fact that Senator Mitch McConnell of Kentucky, the minority leader, did not support him in the primary.