The laws of Connecticut explicitly discrimination against homosexuals, ie the exercising of rights available to the rest of the population. If Connecticut wants to ban gay marriage, they need a constitutional amendment. Despite the fact that CT is the third most Catholic state in the union (after Rhode Island and Massholechusetts), most voters Catholic or otherwise, won’t care enough to fight it.
Can two straight men or two straight women get married in Connecticut? I don't think so. And if not, then no right is being denied to gays, since the straight population doesn't have that right either.
Ultimately it comes down to this: the right that homosexuals seek isn't the right to marry, but rather the right to determine how society defines marriage -- and they don't have a right to that. It's important to frame the argument correctly.
Now it is true that while society has the right to define marriage, it doesn't have the right to define it in a way that denies someone their rights. This is why the miscegenation laws were rightly overturned by the courts. Those laws reflected a definition of marriage that took race into account, and it is a violation of rights to judge people by race.
The gay marriage crowd will then say that defining marriage according to sex is no different than defining it according to race, that these are an equivalent violation of civil rights, but they are wrong. The difference is that whereas race does not determine behavior, sex does -- especially the behavior known as "having and raising children", which society has a particular interest in. Since society has a right to make laws based on behavior, and since sex determines behavior, it may define marriage according to sex.
Therefore, society has a right to define marriage as between a man and a woman. Such a definition does not violate the rights of gays, and gays don't have a right to change it.