Michael Lee said the couple wants to get Utah’s law overturned.
"We would like to have enough exposure to where we can go into a congressman or senator, someone with political clout and present a case sound enough to get the law changed," he told KTVX.
The biggest hurdle to first-cousin marriages is genetics. In 2013, researchers at Columbia University in New York City found that first cousins share 12.5 percent of their grandparents' DNA, while second cousins share only 3 percent.
The Lees started a petition to gain support for changing the law.
Angie and Michael Lee said they have loved each other since they were children.
"No one I've ever been with will make me feel as perfect as she does," Michael Lee told KTVX. "Her being my cousin and some of the responses is a small price to pay."