Fallen, fallen, fallen.
It's ridiculous when you look at it that way. It becomes obvious that you could play the same game with other groups. Left-handed people. The myopic. Men.
Still, I think when people bring up Greece and Rome -- particularly both, since ancient Greece is famous for its homosexual couplings, whereas Rome is not so much, really -- they're telling you something important about how they're thinking and how they hope their listeners are thinking.
They're living in the first century of a dominant empire. Perhaps the last century: political dominance is not known for predictable longevity. And who wants to live in a fallen empire? It can be surprisingly comfortable, but compared to being the top of the heap, especially for a people raised to competition -- no. Americans want to maintain dominance in the world. Preferably permanently.
How does a nation do that? Well, sensible domestic and foreign policies would help; a sound economy would be a positive thing. And how easy is it to achieve those things? Not very. It would take thousands of pages to describe a domestic policy alone, and each point of it would be a matter of some contention: whether it was the right thing to do, whether it was actually achievable, whether it would get its proponents tossed out of office before it could succeed.
On the other hand, if it's the fault of homosexuality that empires fall, and we're worried about the fall of our own empire more than almost anything...well, the solution looks much simpler from that vantage. Stop the gays, lest they bring about the downfall of our country, not just in a moral but in a literal sense.
I'm not trying to claim that this is the dominant cause, reasoning, or justification of opposition to gay marriage. Far from it. It's just a thread that interests me. I have a hard time interpreting the Greece and Rome comments any other way. (Anyone else?) And the thing is, if I tried to do something like this in a story, this combination of memes or motivations would seem unreasonable, unbelievable. I couldn't put similar words into a character in a fantasy or science fiction setting and have it come off as believable.
I really hate it when real people are two-dimensional and inadequately motivated.