Does denying same sex-marriage conflict with the American Dream?

Pre-University Paper from the year 2012 in the subject Didactics for the subject English - Miscellaneous, grade: Sehr Gut Minus (13 Punkte), , language: English, abstract: The dream of an America with boundless possibilities has shaped the American society over centuries. As the historian James Truslow Adams defined the phrase ¿The American Dream¿ in 1931, it is the ¿dream of a land, in that life should be better and richer and fuller for everyone, with the opportunity for each according to ability or achievement¿ and in that everyone should ¿be recognized by others for what they are, regardless of the furtuitous circumstances of birth or position¿.
The idea of the American dream is rooted in the United States¿ Declaration of Independence which declares that ¿all men are created equal, that they are endowed by their Creator with certain inalienable rights, that among these are Life, Liberty and the Pursuit of Happiness¿.
However there are issues like homosexuality and same-sex marriage that, with regard to the ban on same-sex marriage present in most of the United States, seem to be contrary to the notion of the American Dream.
Thus one has to ask: Don¿t gays/lesbians deserve the Pursuit of Happiness and the same rights as heterosexuals? Does marriage fit in as an inalienable right? Or quite simply, does denying same-sex marriage conflict with the American Dream?