“I think the conversation needs to start by acknowledging we aren’t going to deport 12 million illegal immigrants,” said Mr. Paul, a Republican from Kentucky. “If you wish to work, if you wish to live and work in America, then we will find a place for you.”

Though Mr. Paul never used the word “citizenship” in his nearly 18-minute speech, he talked about expanding visas for high-tech workers and giving them priority, discussed issuing “special entrepreneurial visas,” and implied that illegal immigrants would have a path to citizenship that was contingent on securing America’s borders.