“I don’t have any verse and scripture” to back that up, he allows, but he’s got a good feeling about it. And why not? “Jesus” is really just a stand-in in this question for morality writ large, right? If you support SSM you think the practice is moral (I should hope), and if you’re a Christian who believes something is moral, almost by definition you need to believe Jesus thinks so too. There’s nothing doctrinal about this, by Carter’s own admission. It’s just “I feel strongly this is right, ergo God must as well.”
It occurs to me that I’ve never seen a poll on this question, asking religious gay-marriage supporters and opponents whether they think their position lines up with what God would want. That’d be interesting, especially among supporters. Opponents have the passage in Leviticus against homosexuality to stand on but supporters would be forced to either wing it Carter-style or concede that what God wants and what they want as a matter of public policy don’t always line up, a difficult admission for a person of faith. At least one religious person I know who backs SSM justifies it in render-unto-Caesar terms: A church should be free to refuse to perform gay weddings in accordance with its interpretation of God’s will but the state can’t refuse equal rights to all of its citizens on the same grounds, even if a majority agrees that God would disapprove. That solves the church-and-state problem of gay marriage potentially but it doesn’t really solve the WWJD problem. If you honestly believe that God opposes a certain practice, is it permissible to condone it as a matter of state policy (while refusing to participate in it yourself, say)?