But it was clear from the start of the 80-minute argument in a packed courtroom that the justices, including some liberals who seemed open to gay marriage, had doubts about whether they should even be hearing the challenge to California's Proposition 8, the state's voter-approved gay marriage ban.
Justice Anthony Kennedy, the potentially decisive vote on a closely divided court, suggested the justices could dismiss the case with no ruling at all.
Such an outcome would almost certainly allow gay marriages to resume in California but would have no impact elsewhere.
There was no majority apparent for any particular outcome, and many doubts were expressed by justices about the arguments advanced by lawyers for the opponents of gay marriage in California, by the supporters and by the Obama administration, which is in favor of same-sex marriage rights. The administration's entry into the case followed President Barack Obama's declaration of support for gay marriage.
On the one hand, Kennedy acknowledged that same-sex unions had only become legal recently in some states, a point stressed repeatedly by Charles Cooper, the lawyer for the defenders of Proposition 8. Cooper said the court should uphold the ban as a valid expression of the people's will and let the vigorous political debate over gay marriage continue.
But Kennedy pressed him also to address the interests of the estimated 40,000 children in California who have same-sex parents.
"They want their parents to have full recognition and full status," Kennedy said. "The voice of those children is important in this case, don't you think?"
Yet when Theodore Olson, the lawyer for two same-sex couples, urged the court to support such marriage rights everywhere, Kennedy feared such a ruling would push the court into "uncharted waters." Olson said the court similarly ventured into the unknown in 1967 when it struck down bans on interracial marriage in 16 states.