Fresh off his landslide victory at the Washington Times/CPAC presidential straw poll on Saturday, Sen. Rand Paul took an indirect shot at one of his potential 2016 rivals and said the GOP must focus on expansion.

The Kentucky Republican, who captured 31 percent of the vote in the straw poll, said his success largely is due to the support of young Americans who embrace his message of privacy rights and respect for the Fourth Amendment.

He also said that he’s not interested in criticizing other Republicans.

“Everybody has their own style … I don’t spend a lot of time trying to drag people down,” Mr. Paul said during an interview on “Fox News Sunday.” “I don’t spend any time sort of trying to criticize others in the party because I realize the party has to be bigger, not smaller.”

Sen. Ted Cruz, the Texas Republican and rising GOP star who pulled in 11 percent in the straw poll, took shots in his CPAC speech at recent Republican presidential candidates perceived as moderate.

“Of course all of us remember President Dole and President McCain and President Romney,” Mr. Cruz said.

If the straw poll is any real indication, conservatives appear to be favoring Mr. Paul’s approach.

He attributed his popularity to young people concerned that the federal government is intruding into Americans’ private lives with its surveillance and data-collection programs.

“I think young people across the country are fed up with a government that says the Fourth Amendment doesn’t apply to your records, doesn’t apply to your cell phone,” Mr. Paul said. “The youth in particular have lost faith in this president, and so I think there’s a real opportunity for Republicans who do believe in the Fourth Amendment to grow our party by attracting young people and bring that energy into our party.”

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