"Call me cynical, but I wasn't sure his views on marriage could get any gayer," Paul, R-Ky., said this week at a gathering sponsored by the Iowa Faith and Freedom Coalition.
"It did kind of bother me though that he used the justification for it in a biblical reference. He said the biblical golden rule caused him to be for gay marriage. And I'm like what version of the Bible is he reading?
"Now that doesn't mean we need to be harsh and mean and hate people ... . But that doesn't mean that we have to go ahead and give up our traditions. We've got 6,000 years of tradition."
The Los Angeles Times reported Saturday a video of Paul's speech included him telling his audience the traditional family unit needs to be defended.
"The family is a really important thing. We shouldn't just give up on it," he said.
The Times said Palin, the daughter of Sarah Palin, the former Alaska governor and 2008 Republican vice presidential candidate, chided the Democratic president for saying he came to his decision, in part, because his two daughters have same-sex parents.
"We know that in general kids do better growing up in a mother/father home," the younger Palin, who became a single parent as a teenager, wrote in her blog for Patheos. "Ideally, fathers help shape their kids' worldview."