The justices may say as soon as today whether they will hear arguments that the Constitution guarantees same-sex marriage rights.A ruling in favor of gay rights would threaten bans that remain in effect in 14 states.

The country has already undergone sweeping changes since October, when the justices ducked the subject by rejecting seven appeals. The number of states where gays can marry has since surged to 36 from 19, with Florida’s addition this week. That puts more than 70 percent of the U.S. population in a jurisdiction that allows gay marriage, and leaves a less daunting task for those justices inclined toward legalization.

“We are in the end game on the freedom to marry for same-sex couples,” said James Esseks, a lawyer who leads the gay-rights project at the American Civil Liberties Union. “The reality on the ground is that in 36 states same-sex couples can marry, and the sky has not fallen.”

At the same time, legal uncertainty has increased, putting more pressure on the Supreme Court to act. Federal appeals courts are now divided, with four backing marriage rights, one opposing and a sixth preparing to hear arguments in New Orleans today.

The nine Supreme Court justices will have five appeals before them when they meet privately to determine their docket. An immediate decision to take up one or more same-sex marriage cases would probably mean arguments in April and a ruling by late June. The justices also could delay review until their next nine-month term starts in October.

A Supreme Court decision legalizing gay marriage would be a watershed moment for a movement that as recently as 1996 had support from only 27 percent of the American public, according to a Gallup poll. The latest Gallup survey on the subject, conducted in May, showed 55 percent supporting gay marriage and 42 percent opposing.

Gay-marriage supporters have reason for confidence even in a court that has displayed conservative leanings on other social issues, including affirmative action and abortion.

The likely swing vote, Justice Anthony Kennedy, has been a champion for gay rights, writing the court’s 2003 decision that said states can’t criminalize gay sex acts. Kennedy also wrote the 2013 decision striking down the core of the U.S. Defense of Marriage Act, which denied federal benefits to same-sex spouses.

The latter decision, United States v. Windsor, is now the central precedent for supporters of marriage rights. In it, Kennedy said the Constitution protects same-sex couples’ “moral and sexual choices,” and he rejected many of the justifications for treating them differently from heterosexuals.

Opponents of gay marriage, however, point to other parts of Kennedy’s opinion that emphasize the traditional role of states in defining marriage.

“The court should uphold the freedom of Americans to affirm marriage as the union of a man and a woman,” said Jim Campbell, an attorney with the Scottsdale, Ariz.-based Alliance Defending Freedom, which has fought against same-sex unions in four states.

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