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Before the conference, Rand Paul and his office bristled at questions about their most recent public appearance together.

“I think that I have been here long enough that I should be judged for who I am and not necessarily a comparison,” Mr. Paul told The Washington Times over the summer. “How many times did George W. Bush get asked about his father? I think if anything, I am asked more about it than he ever was.”

Vendors at LPAC sold Rand Paul 2016 gear amid conversations about the government’s possible involvement in the Sept. 11 terrorist attacks, and alongside merchants peddling T-shirts casting NSA leaker Edward Snowden as a “Hero” and tank tops that read “I Don’t Dial 911” above the image of a handgun.

“Someone said that Ron Paul speaks to people who see the light and Rand Paul speaks to people who are still in the dark,” said Drew Forbes, a 31-year-old from Houston. “I think that Rand Paul has had better success with a mainstream audience whereas Ron Paul has more success with the idealist, with the pure strict libertarian.”

Mr. Forbes said that Mr. Paul’s job could get easier if voters think that Hillary Rodham Clinton is going to win the Democratic nomination for president.

“I think there are plenty of people who will say, ‘Well he is not a purist. He does not say everything I want him to say.’ But at the end of the day are you going to vote for him or vote for Hillary?” he said.