The next phase of President Barack Obama's evolving position on gay marriage may come Thursday, the deadline for his administration to weigh in on a landmark Supreme Court case that could determine whether same-sex couples have a constitutional right to wed. Gay rights supporters are pressing the administration to file a friend-of-the-court brief urging the justices to overturn California's gay marriage ban. Mr. Obama is not required to file a brief, though he raised expectations in his second inaugural address when he declared that gays and lesbians must be "treated like anyone else under the law." An administration brief would not be legally binding. But it could offer the clearest insight into Mr. Obama's views on gay marriage, which he supports but has said should be governed by the states. On Thursday afternoon, with the filing deadline just hours away, White House spokesman Jay Carney wouldn't say whether the administration planned to file a brief and referred questions to the Justice Department. The Proposition 8 ballot initiative was approved by California voters in 2008 in response to a state Supreme Court decision that had allowed gay marriage. Twenty-nine other states have constitutional amendments banning gay marriage, while nine states and the District of Columbia recognize same-sex marriage. Also Thursday, 13 states, including four that do not currently permit gay couples to wed, urged the court to declare California's Proposition 8 ballot measure unconstitutional. Delaware, Illinois, New Mexico and Oregon joined with the nine states and the District of Columbia that allow same-sex marriage in telling the justices that states encourage marriage because it enhances economic security and emotional well-being for the partners, and is better for children. "All of these interests are furthered by ending the exclusion of same-sex couples from the institution," said the brief signed by Massachusetts Attorney General Martha Coakley and also joined by Connecticut, Iowa, Maine, Maryland, New Hampshire, New York, Vermont and Washington. More than 100 prominent Republicans have also signed a friend of the court brief in support of gay marriage. Among them are former GOP presidential candidate Jon Huntsman and Florida Rep. Ileana Ros-Lehtinen. Gay rights advocates are anticipating the administration filing a broad brief, one that would ask the justices to not only strike down the California measure, but also rule that the Constitution forbids any state from banning same-sex unions. But the administration could also file a narrower brief applying only to California. Even the latter brief would appear to mark a shift away from the president's contention that states have the right to determine whether to allow same-sex marriages. While an administration brief alone is unlikely to sway the high court, the government's opinion does carry weight with the justices. Solicitor General Donald Verrilli would formally file a brief, though he has been consulting with White House officials. And it's almost certain that Obama, a former constitutional law professor, made the administration's final decision. In his inaugural address, the president said the nation's journey "is not complete until our gay brothers and sisters are treated like anyone else under the law." "For if we are truly created equal, than surely the love we commit to one another must be equal as well," he said. Mr. Obama has a complicated history on gay marriage. As a presidential candidate in 2008, he opposed the California ban but didn't endorse gay marriage. As he ran for re-election last year, he announced his personal support for same-sex marriage but said marriage was an issue that should be decided by the states, not the federal government. Public opinion has shifted in support of gay marriage in recent years. In May 2008, Gallup found that 56% of Americans felt same-sex marriages should not be recognized by the law as valid. By November 2012, 53% felt they should be legally recognized. The Supreme Court will hear oral arguments in the Proposition 8 case on March 26. One day later, the justices will hear arguments on another gay marriage case, this one involving provisions of the federal Defense of Marriage Act. The act defines marriage as between a man and a woman for the purpose of deciding who can receive a range of federal benefits. The Obama administration abandoned its defense of the law in 2011 but continues to enforce it. In a brief filed last week, the government said Section 3 of DOMA "violates the fundamental constitutional guarantee of equal protection" because it denies legally married same-sex couples many federal benefits that are available only to legally married heterosexual couples.