In his majority opinion on the case, Justice Kennedy wrote that "to oppose gay marriage is to deny dignity to people who deserve equal protection."

Speaking on NBC's "Meet the Press," DeMint, an opponent of gay marriage, pushed back against Kennedy's ruling.

"He is denying dignity to the millions of Americans who, for moral or religious reasons, believe that gay marriage is wrong," DeMint said.

The Supreme Court's decision to overturn DOMA has sparked considerable backlash among social conservatives. In Congress, Rep. Tim Huelskamp (R-Kansas) plans to introduce a constitutional amendment to define marriage as a union between one man and one woman.

Appearing on the NBC, Huelskamp expressed opposition to gay marriage, saying it is detrimental for children to grow up with two parents of the same sex.

DeMint echoed those concerns, asserting that it's "been proven" that marriages between a man and a woman are "the environment where children can thrive and succeed."

"So it's not about the desires of adults, it's really about the best environment for children," he said.

"We're talking all about politics, but the reason governments at the state level and the federal level have recognized marriage between a man and a woman is because it's better for our country and it's better for children."