Mr. Paul has so far earned 50 delegates, according to the A.P. tally, and the campaign hopes efforts to obtain more delegates at state party conventions will mean he will have 150 to 350 delegates bound to him for the convention. Aides also believe he will ultimately win enough delegates to satisfy the five-state nominating threshold, as supporters pack state party gatherings in coming months and battle to select national delegates loyal to Mr. Paul in proportions greater than the percentage of votes he received.

“There is a lot of stuff in motion,” he says. “This is what people don’t know about yet.”

Whether he will use those delegates to help Mr. Romney is an open question. Mr. Paul demurs when pressed on whether he would help Mr. Romney, a former Massachusetts governor, should he fail to clinch the nomination on the first try, saying, “I haven’t thought much about that.”