When it rules, the court could strike down laws across the country banning same-sex marriage, or it could leave the current patchwork of state laws in place, choosing to let state legislatures and state courts sort it all out.
"This was a deeply divided Supreme Court, and a court that seemed almost to be groping for an answer here," CNN Senior Legal Analyst Jeffrey Toobin said after the arguments.
Four of the more liberal justices seemed at least open to the idea that same-sex marriage should be allowed in California. Three of the more conservative justices seemed aligned with the view that marriage should only be for a man and a woman, and it's likely they'd be joined by Justice Clarence Thomas, who doesn't speak at arguments.
That could leave Kennedy as the swing vote, as has often been the case.
While admitting the law's defenders are "not just any citizens," Kennedy raised concerns about whether just the possibility of same-sex marriage was enough to establish they had suffered harm -- a key jurisdictional hurdle allowing them to appeal in the first place.
Nine states permit same-sex marriage
Among the 41 states that now forbid same-sex marriage, nine of them allow civil partnerships. Nine other states allow same-sex marriage, and about 120,000 same-sex couples have gotten married, according to estimates.
Prohibitions seem to run counter to polls that show rising support overall for same-sex marriage.
A CNN/ORC International poll released on Monday found 53% of Americans now support same-sex marriage, up from 40% in 2007. As to how the federal government should handle the issue, another CNN/ORC International poll out Tuesday found 56% of the public feels the federal government should also legally recognize same-sex marriages.