"Most" Americans are too shallow and disinterested to have a cogent opinion on the subject. This goes in spades for most people who were born after 1980.
There are many reasons why the state legislatures might decide that they will sanction same-sex marriages in pretty much the same way that they sanction normal marriages. There are many reasons why this is stupid, but that's up to the legislature to decide, and I have no problem if they decide differently than I would.
As for the United States Supreme Court, marriage is a STATE issue entirely, and the only Federal concerns are that all the states and the Federal government recognize the legitimate actions of the other states. Specifically, that if a state recognizes a couple as married, the Feds and the other states must acknowledge this status when a legal issue arises within their jurisdiction.
But as for the "Right of Privacy" and the "Constitutional" right to marry someone of the same gender, these are patent nonsense. There is no right of privacy in the Constitution, and although there are privacy interests that are protected by the Fourth Amendment, a "right" that would encompass various forms of homosexual sodomy is pure fiction.
If such a "right of privacy" existed, then it is absolutely certain that plural marriages would also be protected, as would incestuous marriages (adults only), and probably inter-species marriages...you know how much single women LOVE their dogs.
We have had "gay marriage" for several years now, and while it is a part of our society going to shit, it's probably been no more harmful than everything Kardashian.