A quick Google search found this speech, Homosexual Marriage?, that Senator Byrd made in 1996, during the debate over the Defense of Marriage Act. His speech ends with these words: "I say to my colleagues, let us take our stand. The time is now. The subject is relevant. Let us defend the oldest institution, the institution of marriage between male and female, as set forth in the Holy Bible. Else we, too, will be weighed in the balances and found wanting."

But on the other hand, to be fair to Senator Byrd, both John Kerry and John Edwards, who would vote against the constitutional amendment to ban gay marriages, say that they are opposed to gay marriage -- but that it should be left to the individual states, not to the federal government. I doubt, however, that they would invoke the authority of the Bible to oppose gay marriage.