This article in The State notes that, as recently as 2006, a referendum on a constitutional amendment to ban gay marriages passed 78% to 22%. And another poll by Winthrop in 2006 found that 73.5% of South Carolinians supported adding the prohibition to the state constitution. More recently, other polls by Public Policy Polling have shown opposition to gay marriage falling fairly rapidly in the state in the last three years. But none of the polls have shown the number as low as this recent standing.
Now it's hard to say what the most conservative state in the country is. Idaho and Wyoming conservatism is different from Deep South conservatism. And earlier this year Nate Silver used various statistical evidence to argue that either Alabama or Mississippi would be the last states to give way on equality. But South Carolina is about as conservative as states come, especially in terms of the fundamentalist bible-drenched brand of conservatism which is the sheet anchor of hardcore opposition to same sex marriage.
And yet even here, likely within a few years, support for same sex marriage will likely be the majority position. That's great for full civic equality. But it's perilous for the political fortunes of equality opponents. Remember, just today John Boehner announced that he opposed the ENDA workplace civil rights bill, even though it's sailing through the Senate. That looks to soon be a minority and just as importantly politically and generationally isolating position.