This issue, although more popularized than in the past, is still quite controversial. The Proposition 8 case is about whether or not states, specifically California, have the authority to deny marriage to same-sex couples.
A quick rundown for those who don't know or don't remember : California in May of 2008 made same-sex marriages legal via court ruling in, In re Marriage Cases. Before this ruling could take effect, a petition was started to put the idea of same-sex marriage on the voting ballot. So from June to November of 2008 same-sex couples flocked to California and were getting married: one such couple was Ellen Degeneres and Portia de Rossi. In November Proposition 8 was passed with a 52% majority and effectively stripped the right from same sex couples. This ruling was challenged and was struck down in California courts, in the District 9 Court and has now made its way to SCOTUS.
Prop 8 has been challenged under the basis of the Equal Protection Clause in the US Constitution. This is found in the 14th ammendment and states: "no state shall ... deny to any person within its jurisdiction the equal protection of the laws." This line of argument would say that the State does not have the right to discriminate or treat same-sex couples differently than opposite-sex ones without a significant interest in doing so.
So far this defense has held in the courts, as thus far no coherent argument has been made to give an interest in this discrimination. Some people may say "This isn't discrimination! Same-sex couples have the same marriage rights as opposite-sex ones. They can marry a person of the opposite sex." This though however does not seem to be the case. Opposite-sex couples have the right to marry the person of their choosing; to marry the person whom they have a romantic attraction to; to marry the person whom they have sexual attraction to; and to marry their life partner. Same-sex couples, having only the right to marry someone of the opposite sex, have only one of those components of the right - namely they can marry a person of their choice as long as that person is not the same sex as them. The rest does not apply.
I think we can all agree that it is discriminatory to not allow same-sex couples to marry, and so on then there must be some legitimate purpose for the state to be able to discriminate. The popular defenses are: religion, children, procreation, and the moral fabric of society.
Religion, as we have seen in the past, has no place when discussing public law. You can't legally object on religious grounds when discussing if something should or shouldn't be law. Religion and State are separate in the US, as it is a secular government, therefore as soon as you say something about your religion and the potential law the judges can disregard what you said (unless the law is specifically about religion). The only argument to be made using religion is to question how this law will affect your religious freedom. Many, many experts have already said that churches will not be forced to marry same-sex couples; just as churches are still not legally required to marry interracial couples.
The claim that same-sex couples being allowed to marry will rip apart the moral fabric of society tends to go back towards the religion argument; however, there are some atheists and agnostics who also try to use this line of reasoning. If it were true that same-sex couples marrying would rip apart society's morals and endanger the population then it may be 'justified' to discriminate, but there is no evidence to back this claim. Looking to other countries which have legalized marriage equality we don't see people running around doing anymore more or less horrible than we see here- and some of those countries have had marriage equality for over a decade.
The above line of reasoning usually relies on the slippery slope argument. This line of reasoning and argumentation is fallacious and really has no bearing on the validity of the arguments on the topic being discussed. Many people say that the legalization of same-sex marriages will lead to zoophilic marriages (animal-human marriages), incestuous marriages (those between first cousins are legal in some states), and even pedophilic marriages (those under 18 can already marry as long as they have permission from the legal guardian(s) of the minor(s) in question). The problem with the slippery slope argument, especially in relation to this subject, is that it fails to account for additional factors with different problems and as such is inherently flawed.
Because of much of the above, Prop 8 has been struck down repeatedly in the lower courts and I would expect it to be struck down in SCOTUS as well. There is always the possibility of SCOTUS saying that the law isn't discriminatory, however that is extremely unlikely.