TRENTON — There’s no mention of New Jersey in either of the two gay marriage cases set to go before the U.S. Supreme Court on Tuesday, but the state could be directly affected by both rulings, especially if the justices opt to strike down California’s ban on the practice.

In that case, which challenges the constitutionality of Proposition 8, the 2008 voter initiative that ended same-sex marriage in California, the U.S. Justice Department is arguing that the court should extend gay marriage to states that already allow same-sex couples to enter into civil unions. The government’s argument is that these states — which include New Jersey — can’t have it both ways, offering some of the benefits of marriage to gay couples while keeping them from getting legally married.

The second case is a challenge to the Defense of Marriage Act, which forbids the federal government from recognizing gay marriages.

The Supreme Court is set to hear both cases at a critical juncture in the same-sex marriage debate. The latest national poll released last week shows that 58 percent of voters believe gay Americans should be allowed to wed. Nine states and the District of Columbia now sanction same-sex marriages, and a measure that would extend that right is nearing a crucial vote in to the Illinois Legislature.

New Jersey is one of seven states that allow gay couples to enter into civil unions.

Theodore Ruger, a University of Pennsylvania law professor not involved in the litigation, expects the court to take an incremental approach that could strike down both laws but still leave many questions to be resolved in courthouses and in state houses across the country.

That would be in keeping, he said, with the approach of Justice Anthony Kennedy, who is perceived as the court’s swing vote on civil rights issues.

“It’s quite plausible that Kennedy would write a middle position,” Ruger said.

In New Jersey, Gov. Chris Christie vetoed a same-sex marriage bill last year. He has said that tougher enforcement of antidiscrimination laws could address any problems with civil unions. Democratic lawmakers, meanwhile, have rejected Christie’s suggestion to put the question of gay marriage on the ballot, saying civil rights questions should not be subject to a vote.

Also in the mix is a 2011 case filed by Garden State Equality that asks a state Superior Court judge in Mercer County to order the state to allow gay marriages. No trial date has been set.

If the U.S. Supreme Court does strike down Proposition 8 or the Defense of Marriage Act, Garden State Equality attorney Lawrence C. Lustberg said, that would bolster his arguments in New Jersey.

The key, he said, is whether the court accepts another Obama administration request and grants gay couples additional constitutional protections known as “strict scrutiny,” which it could do under a more incremental ruling.

In that scenario, it’s much less likely that New Jersey courts would accept the state attorney general’s argument that gay marriages buck established traditions and thus should not be judicially mandated, he said.

“It seems to me extremely unlikely that that state interest could survive a strict scrutiny test,” Lustberg said.

The New Jersey Attorney General’s Office, which is arguing the case against gay marriage, declined to comment for this article.

Opponents of gay marriage hope the administration’s strategy will fail and a more conservative ruling from the high court could blunt efforts by gay-rights advocates at the state level, said John C. Eastman, director of Chapman University’s center for constitutional jurisprudence and chairman of the National Organization for Marriage, which will be defending Proposition 8 before the Supreme Court.

State courts, including those in New Jersey, won’t be as receptive to arguments to legalize same-sex marriage if the U.S. Supreme Court finds there isn’t a constitutional right to it, Eastman said.

“It would certainly lend strength to the arguments on the other side,” he said. “There’s a decent chance that that argument by the Department of Justice backfires.”

In the Mercer County case, Garden State Equality is arguing that civil unions haven’t lived up to the New Jersey Supreme Court’s mandate in 2006 requiring that same-sex couples be allowed to enter into such unions and that they be treated the same as their heterosexual counterparts in the eyes of the law. At the time, the court declined to require the legalization of same-sex marriage, saying that decision should be left to the Legislature.

The state, for its part, is countering that civil unions strike an appropriate balance between granting same-sex couples important legal rights while still preserving the traditional definition of marriage.

Gay-rights advocates expect the case to eventually reach the state Supreme Court, where they hope to prove that civil unions have not been privy to the state’s strong constitutional protections.