“I feel better about it,” Ms. Denis said the other day, explaining how it took some time for her to see her cousin as someone who could lead the country. “He’s very knowledgeable. He studies. He knows what’s going on in the world.”

Ms. Slider tends to be the one who galvanizes the cousins — dozens of first, second and third cousins of Mr. Rubio’s are scattered in and around Las Vegas — to come to his campaign events.

“We came from the same people. How do we see it so differently?” she said, laughing off the family’s political differences. “In the end, we all hug each other.”

Sometimes, like at his rally on Sunday, there are so many cousins who come to see him that the campaign will reserve a section for them near the front. And sometimes, there are so many of them he does not have time to greet them all. He left the casino on Sunday night and rushed back to his hotel without saying hello.

Given their impressive numbers, Mr. Rubio said he has had to deliver a reminder to his staff on occasion: If someone walks in without a ticket saying they are one of his cousins — even if they have blue eyes or blond hair — they probably are.