The nine judges of the US Supreme Court will decide next week whether to consider the constitutionality of same-sex marriage – a keenly awaited choice that will have far-reaching implications for thousands of legally married gay couples across the United States.

Activists are hoping that shifting public opinion on the issue, most recently demonstrated by election-day victories in all four states where same sex-marriage measures were on the ballot, will convince the judges to take on the issue.

Up for decision is a set of cases relating to the Defense of Marriage Act (Doma), a 1996 law which states that every time any federal law refers to marriage, it means only that between a man and a woman. Same-sex couples who are legally married in one of nine states or Washington DC are thus denied the benefits or opportunities afforded by marriage to opposite-sex couples.

Five federal courts have ruled that Doma is unconstitutional. The Supreme Court could decide to take on one or more of these cases. The judges will also decide whether to consider an appeal from supporters of California's Proposition 8, a voter-approved amendment to the state constitution which seeks to ban same-sex marriage. Another petition before the justices relates to the state of Arizona, which is seeking to revive a state law that is similar to Doma.

Four Supreme Court justices must agree a case in order for the court to take it. They can take up all of the measures before them, none of them or some. The justices are expected to announce a decision on 30 November.

Advocates of marriage equality are hoping that the tide of public opinion that has been demonstrated by polls over this year will persuade the justices to strike down Doma. Last year, the Obama administration decided not to defend the law in court, believing it to be unconstitutional.

Brian Moulton, legal director of Human Rights Campaign, a marriage-equality group, said that the election-night victories had underlined the need for a Supreme Court decision on Doma, because of the growing number of couples who will be affected by a federal law that discriminates against them.

Moulton said: "The number of couples who are married at the state level who will not be recognised because of Doma will get bigger and bigger, so the scope of the problem will grow. That might influence the question of whether to resolve the issue."

He said he was optimistic that the judges would decided to take up the issue: "The justices are people as well and they read the newspapers. That gives them a sense of where the country is going on these issues."

Two of the Doma cases, both brought against the federal office of personnel management, relate to the denial of healthcare benefits to same-sex spouses. Gill v United States Office of Personnel Management is from the First Circuit in Boston and Golinski v OPM is from the Ninth Circuit. In each of these cases, the Court of Appeal held that Doma violated equal protection rights.

Gill was considered with another Doma case, Massachusetts v United States Department of Health and Human Services, in which the First Circuit Court of Appeals ruled that Doma's denial of federal recognition to lawfully-married same-sex couples violated the US constitution's guarantee of equal protection of the laws.

The Supreme Court is widely expected to take one of the cases, but predicting an outcome is difficult. If, for instance, the Supreme Court declines to take the Gill and Massachusetts cases, the First Circuit decision would stand. However, it would apply only to the states in that Circuit – Maine, Massachusetts, New Hampshire and Rhode Island.

Douglas Nejaime, an associate professor at Loyola Law School in Los Angeles, said Doma was important but pointed out that it does not have wider implications for states where same-sex marriage is illegal.

Nejaime said: "The reason that the popular vote on election night figures into this is it shows the court that more states are recognising same-sex marriage. If they overturn Doma it just means that those couples will be recognised federally. It wouldn't have any impact on states where they don't recognise same-sex marriage."

More controversial, he said, was the question of whether the justices decide to take on Proposition 8. It is exclusive to California, so it is less likely the justices will take it up. Both a federal trial court and the Ninth Circuit Court of Appeals have ruled Proposition 8 unconstitutional. However, the Ninth Circuit found that it was the unique circumstances of California that made adopting Proposition 8 a violation of the US constitution.

If, as many predict, the justices decline to consider an appeal from supporters of Proposition 8, same-sex couples would again be permitted to marry in California, as was the case for a few months in 2008 before the passage of the proposition. Because of the size of the state, such a decision would at a stroke dramatically boost the number of gay couples in the nation who would be able to legally marry.

Nejaime said that the court had several options regarding Proposition 8, including upholding it along the narrow focus of the Ninth Circuit ruling. "If they went behind the Ninth Circuit, we would only have same-sex marriage in states that already have domestic partnerships or civil union. The broadest ruling would be to say all of the states where same-sex marriage is not allowed is unconstitutional – but I don't think the court is ready to go there."

If the justices decide not to take the case, California could begin issuing marriage licences within days.

Wendy Goffe, a lawyer in Seattle who has written on the issue, also believes that the justices will decline the Proposition 8 case.

Goffe said: "I'm not convinced they would take it because the Supreme Court [is] very much in support of state rights."

Citing the decision by the Supreme Court in January to uphold controversial parts of an immigration law in Arizona, she said: "If you look at the Arizona decision – where they took that and upheld the case and that is a terrible law, but they said it's not our place to mix in with the state. The only way they might pick up Prop 8 is if they make a decision to take all the cases before it. But that would lead to a big mess. It could take decades."

• This article was amended on 26 November 2012. The original described Brian Moulton as the legal director of Human Rights Watch. His organisation is Human Rights Campaign.