Indeed, the advocates argued to the Iowa Supreme Court that same-sex marriage would hurt opposite-sex marriage. The Court asked a simple question, "In what way?" There was no answer to this question that could withstand even modest scrutiny, and as far as I can tell there remains no reasonable answer today. Some people feel that they have been hurt by the ruling, but they are unable to say how.
There is a thread on this over in Social Issues, where I have pointed out that they DO say how they have been harmed. It is usually something like, "Gay marriage would tell my kids that homosexuality is acceptable, but our religion says it is wrong."
(admittedly, that isn't really harm to heterosex marriage, but to heterosexual parents)
Of course, translated, what they are saying is, "Gay marriage would undermine my attempts to teach my kids that homos are evil." It's not a surprise that this argument doesn't hold up in court.
It also begs a lot of questions about society. TV shows, for example, also show homosexuality to be normal. The state allows that, too. In the end, the biggest problem these people face is the fact that homosexuals really AREN'T evil, outside of a "God hates fags" perspective. As homosexuality becomes more commonplace in today's society, it becomes more and more apparent that they aren't a problem. This is the thing that scares the anti-gay people more than anything. Kids these days are so used to seeing homosexuality all over that they don't care, and they can't see what all the fuss is about.
It's pretty obvious why the anti-gay crowd in Iowa is adament about getting it banned NOW. They realize that if they wait even a couple of years with legal gay marriage, everyone will realize that Iowa has NOT been swallowed up by God's minions, and, in fact, gay marriage is no big deal. Shoot, even after 5 years most citizens of Iowa still won't know any married gay couple. How can anyone believe that it is a problem when most people don't see any difference?
As I said, the anti-gay people know that when this happens, they don't have a prayer in the world of stopping it. So act now with predictions of doom before reality has a chance to get in the way.