Black already said he won't require Ohio to perform marriages and just recognize them from out of state, so unless we get a SCOTUS ruling, there actually is a side chance for hope for a stronger marriage equality amendment because
FreedomOhio and EqualityOhio are joining forces (just days after FreedomOhio submitted the original amendment) to create a new petition that would eliminate the religious institutions provision and legalize same-sex marriage in Ohio. It would need 385,000 new signatures by July 2nd and DeWine's approval to get on the ballot this year. There's also a petition circulating statewide that requires about 115,000 signatures to force a state legislature vote on the Equal Housing and Employment Act (basically ENDA on a state level), and if it presumably fails to pass in the legislature, then another 115,000 are required to get it on the ballot.
And appeal or not, Kasich already hurt himself when he appealed Black's ruling that demanded Ohio to recognize a gay marriage from MD in which one of them was on their deathbed. This appeal will only further hurt him among independents, moderates and young voters and even if he did accept the ruling, this would only further anger the far-right (which Kasich has done enough already) and cause more defections to Tea Party-backed Earl in November. As for the Democratic response,
Ed FitzGerald is already capitalizing on the opportunity to make this a decisive issue.