Marriage is between an man and a woman. Loosening the definition of marriage would open up the door to polygamist, polyamorous, or even incestuous relationships, as those groups will be able to use the example of same-sex marriage to point out what would be a hypocrisy in the government's marriage policies. If one deviation from the formula of "one man and one woman" is allowed, other groups will inevitably come forth with similar claims of 'inequality' in how they are treated by the government. Furthermore, every society throughout history has kept marriage between the opposite sex, even in societies where homosexuality was tolerated. There is no good reason why it should change.
The right to marry anybody one chooses is a human right. How can people tell someone who not to marry - if you're in love, you're in love. How many failed marriages have happened between heterosexuals and now people are trying to ban gay people from getting married and trying it out for themselves. It's discrimination and that is against the american constitution in the first place; so no, gay marriage should not be banned by the american constitution.