The Supreme Court will hear arguments this week in two cases that have the potential to transform American society and the status of gays and lesbians in it.

In oral arguments on Tuesday morning the 9 justices will consider whether California’s voter approved ban on gay marriage, Proposition 8, unfairly discriminates against gay people. On Wednesday, they’ll consider whether the 1996 Defense of Marriage Act barring the U.S. government from recognizing same-sex marriages, even in states that allow them, constitutes federal overreach.

Both cases could change the everyday lives of gay people and transform the larger, decades old gay rights movement, which has pursued both a court-based and political strategy to gain more legal protections for gay people. But the California Prop 8 case in particular, called Perry v. Hollingsworth, is considered by both pro and anti-gay marriage camps to be the most important, and potentially sweeping, of the two.

In Perry, there's a possibility that the court could declare that gays and lesbians have a fundamental right to marriage just as heterosexual couples do. Such a decision would send a message from the court that both same sex and heterosexual relationships must be treated equally in the eyes of the law.

“There aren’t many Supreme Court decisions that have the potential to be as transformative,” said Erwin Chemerinsky, founding dean of the University of California Irvine School of Law.

If the court finds a right to marriage for gay people, Chermerinsky said, “it will matter enormously in the lives of millions of gays and lesbians in terms of their ability to marry and it also would be a very profound statement of the court that gays and lesbians are subject to equal protection under the law.”

John Eastman, a law professor at Chapman University and chairman of the National Organization for Marriage, also sees the potential for big, but negative, changes should the court decide to invalidate Prop 8. He says a Supreme Court decision in favor of gay marriage will "forever sever the ties between marriage and children" and discourage heterosexual couples from marrying.

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“It's hard to imagine a more compelling interest than the survival of the species," Eastman said of why the government should be able to limit marriage to opposite sex couples. "We would survive in a way, but without the institution of marriage...you commodify children when you take away the intimate family structure.”

Just 40 years ago, the Supreme Court tersely refused to hear a case brought by a gay couple who wanted to get married in Minnesota, writing that that their claim raised no significant legal issue. At the time, legal opinions often treated homosexuality as criminal, sexually deviant behavior rather than involuntary sexual orientation.

Justice Anthony Kennedy, the current court's conservative-leaning swing vote, departed from that tone when he wrote the 2003 Lawrence v. Texas opinion striking down state sodomy laws. Gay people have a right to privacy in their own homes to practice whatever consensual sexual behavior they wish, Kennedy wrote, in a decision that substantially expanded gay rights in the U.S.

Advocates hope that decision may mean Kennedy will side with them on marriage this time around.

No one knows how broadly the justices will rule, but the fact that they voted to take both the DOMA and Prop 8 cases at once signals that at least some of the justices may want to settle the question once and for all, by either affirming gay couples’ right to wed or shutting down entirely their constitutional claim to marriage.

California voters passed Prop 8 in 2008, after thousands of same-sex couples had already tied the knot under a state Supreme Court decision legalizing gay marriage. If the U.S. Supreme Court upholds Prop 8, it will be a victory for the traditional marriage movement and will further cement the dozens of state voter-approved gay marriage bans that have passed in the last decade.

Many courtwatchers believe Kennedy and the four liberal justices will band together to take an incremental step that affirms gay marriage only in California or just a handful of states without going so far as to strike down the laws in 41 states that ban same-sex marriage. Such a sweeping move could spark a backlash, and seems unlikely since the justices have several other options open to them.

More modest legal options include striking down Prop 8 on narrow grounds that only affect California or striking down Prop 8 in a way that only affects the eight states, including California, that allow civil unions but not gay marriage. That "eight state" argument is advanced by the Obama administration, which argued in its brief to the Supreme Court that a state has no legitimate interest in offering gay couples all the benefits of marriage in a civil union but withholding the title of marriage.

The justices could also rule that the supporters of Prop 8 don’t have the legal right, or standing, to appeal the lower courts’ decision striking down Prop 8, which would make gay marriage legal in California by default. (The defenders of Prop 8 must prove to the justices that they will suffer a direct injury if the gay marriage ban is struck down in order to have standing to appeal the case to the Supreme Court.)

Loyola Law Professor Doug NeJaime said he thinks a limited ruling from the court is most likely.

“Things are accelerating so quickly that it seems like it’s an opportune moment for the court to just be nudging that movement forward rather than making a really decisive move,” NeJaime said, pointing to public opinion polls that show a majority of Americans now support gay marriage. “Instead they would just be allowing that momentum to continue.”

The strength of the message sent by the court on gay rights also depends on the language of the opinion. Theoretically, the justices could strike down Prop 8 without even mentioning gays and lesbians’ rights as a class or substantially addressing their claims that they are being unfairly excluded from the institution of marriage.

If the justices decide the supporters of Prop 8 don’t have the legal standing to appeal the lower courts’ decision striking down the ban, they could avoid the controversial issue of same-sex marriage altogether in their opinion.

But even that sort of decision would have a big impact, as gay couples in California—the most populous state in the country—would be allowed to wed. The court would have also decided its first gay marriage case in a way that affirmed gay rights, however narrowly, which would encourage gay rights advocates to continue trying to pass gay marriage on the local level.

“In the specific it would allow them to get married,” Chemerinsky said of a decision that struck down Prop. 8. “In the more abstract it would say no longer are they regarded by the law as a deviant. They’re regarded as equal human beings under the law. “