LGBT Think Progress reports what happened:
Kasich was asked if he could imagine a situation that might cause him to change his position.“I really can’t see one, I mean, I talked to Rob and encouraged him,” Kasich said. “If people want to have civil unions and have some way to transfer their resources, I’m for that. I don’t support gay marriage.”“I’ve got friends that are gay and I’ve told them ‘Look, (same sex marriage) is just not something I agree with’ and I’m not doing it out of a sense of anger or judgment, it’s just my opinion on this issue.”“I just think marriage is between a man and a woman, but if you want to have a civil union that’s fine with me,” Kasich said.
But then a mere 10 hours later, Gov. Kasich's spokesperson "clarified" Kasich's position:
The governor's position is unchanged. He opposes gay marriage and opposes changing Ohio's Constitution to allow for civil unions," said Nichols. "He's opposed to discrimination against any Ohioan and, while he may have used the term 'civil union' loosely in this instance, he recognizes the existing rights of Ohioans to enter into private contracts to manage their personal property and health care issues."It should be noted that the Governor is up for re-election in 2014 and that Ohio's constitution bans both marriage as well as civil unions ("a legal status for relationships of unmarried individuals that intends to approximate the design, qualities, significance or effect of marriage").
This is a position opposed by the vast majority of Ohioans and Americans, with roughly two-thirds supporting some legal recognition for same-sex couples and about one-quarter banning any recognition under the law.