This is a cynical and short-sighted view.
It is cynical because it sees civil rights as a zero-sum game.
It is short-sighted for a closely related reason. Most opponents of gay marriage don't even want to draw a distinction between the religious institution of marriage and the civil institution. In their minds, marriage is divinely ordained, and its earthly recognition in the law is completely natural. "The family" -- meaning their particular conception of what families should be -- is all but sacred.
The gay marriage movement chips away at this belief system in several ways. First, it gives people reason to distinguish between religious and civil marriage; to see that whatever their personal religious beliefs may be, the law is about civil marriage. Also, it presents a picture of marriage as a human creation, rather than divinely ordained. It brings people into contact with unfamiliar family structures. And it makes ideas acceptable or at least debatable that previously were generally rejected. You can see this already with the debate over poly marriage.
In short, if you want to start a singles' rights movement, you should support gay marriage, because emotionally it is moving society in the direction you want, even if it is not yet doing that structurally.