Fourteen states allowed same-sex marriage when Cleopatra De Leon and Nicole Dimetman filed a lawsuit late last year challenging Texas’ constitutional ban on marriages that are not between a man and a woman.

The couple, married in Massachusetts in 2009, lives in Austin and collided with Texas law when they could not both be listed on the birth certificate of their first child. They hope the law is changed before the birth of their second.

“There are moments in our lives that are flashbulb moments,” De Leon said during a town hall event last week, describing the decision she and Dimetman reached to challenge the state’s same-sex marriage ban.

With the case heading to the U.S. Court of Appeals for the 5th Circuit in New Orleans next month, De Leon, Dimetman and gay rights advocates are holding their breath, hoping that Texas is on the verge of its own flashbulb moment. A federal district judge has already ruled in their favor, and if Texas’ appeals fail, the state may be compelled to join the almost three-quarters of the country that now allows same-sex marriage.

That sort of societal change would come at a time when Texas, the largest state with a same-sex marriage ban, is ushering in a new slate of Republican leaders and lawmakers with an even more conservative bent, including staunch opposition to gay marriage.

“There is such a body of legal precedent now,” said Chuck Smith, executive director of Equality Texas, a gay rights advocacy group. “That all sort of collectively reaches the conclusion that the 14th Amendment of the United States Constitution applies to gay and lesbian people as well.”

That is the argument that De Leon and Dimetman are pursuing, citing the birth of their first child, whose birth certificate allows only one parent’s name because the state does not recognize their union.

In February, U.S. District Judge Orlando L. Garcia ruled that the state’s ban was unconstitutional because it “violates plaintiffs’ equal protection and due process rights.” Anticipating an appeal, Garcia stayed his ruling, leaving the ban in place while the case works its way through the courts.

Gay rights advocates, citing a raft of other recent court decisions, believe the conservative 5th Circuit may swing their way.

Conservative activists say that is improbable, and would be at odds with the beliefs of state voters, who handed Republicans an even wider margin of control in the November election.

Gov.-elect Greg Abbott has defended the same-sex marriage ban as attorney general, and Lt. Gov.-elect Dan Patrick, a state senator and Tea Party darling, was among 63 state lawmakers who signed a federal brief arguing that legalization of same-sex marriage could lead to the legalization of bigamy and incest.

Abbott’s office has argued that the courts should respect a state’s sovereignty and not overrule Texas voters, 76 percent of whom voted in 2005 to define marriage in the state’s constitution as “solely the union of one man and one woman.”

In a brief filed with the 5th Circuit, the attorney general’s office also argued that the same-sex marriage ban was in line with the U.S. Constitution’s equal protection clause, which mandates that laws “be rationally related to a legitimate state interest.”

Texas Republicans have long made their opposition to overturning the state ban clear. 

“I think it’s important, when people talk about the momentum, for them to look at the election we just had,” said Jonathan Saenz, president of the conservative group Texas Values, adding that an adverse court ruling was likely to lead Republican lawmakers to “address that” during the next legislative session, which begins in January.

With almost a decade passed since voters approved the ban, Texas gay rights advocates argue that times are changing in this reliably red state, pointing to polling data by Equality Texas that indicates a majority of Texans now favor legal recognition of same-sex couples.

“Nowhere in my stream of consciousness did I consider this would even be where it is right now,” said Victor Holmes, who with his partner, Mark Phariss, is serving as a co-plaintiff in the case. “People know people who are gay now. It’s not those people over there anymore. It’s actual people that they know and they love.”

As a steady stream of states has begun allowing same-sex marriage, either by choice or through court decisions, impatience is growing among those who believe Texas will inevitably be forced to join their ranks.

After the 5th Circuit agreed to expedite consideration of the state’s appeal, the plaintiffs asked Garcia to lift his stay. In anticipation, county clerks in Bexar, Dallas and Travis counties said they were prepared to issue marriage licenses to same-sex couples, and some promised to extend their hours to accommodate an expected influx of couples looking to wed.

Garcia eventually declined to lift the stay, saying it would open the doors to “confusion and doubt” as the appellate court considered the case.

A three-judge panel of the court, which includes 10 Republican-appointed judges and five Democratic appointees, will hear arguments. The panel has not yet been announced.

The Texas case is among dozens of challenges to state same-sex marriage bans that cropped up after the U.S. Supreme Court struck down part of the federal Defense of Marriage Act in 2013. The cases have barreled through the judicial system, with the Texas case among the last to be heard at the appellate level.

All but one appellate court has ruled against bans on same-sex marriage. The sole dissenter, the Cincinnati-based 6th Circuit, created a split with other appellate courts on the issue in November, making it likelier that the Supreme Court will have the final word.

Depending on how quickly the Supreme Court moves, one of the legal challenges could be taken up as early as January, with a decision next summer.

Many legal experts consider it unlikely that the Supreme Court will uphold same-sex marriage bans, citing the court’s action earlier this year when it declined to consider appeals from supporters of same-sex marriage in other cases. By declining to hear the cases, the court allowed same-sex marriage to stand in five states.

“It’s hard to imagine that now, after allowing that to happen, that the court would say there is no right to same-sex marriage,” said Aaron Bruhl, an associate professor of law at the University of Houston who studies federal courts. “I think the court has, in a way, tipped its hand on what the final outcome would be.”

Disclosure: The University of Houston is a corporate sponsor of The Texas Tribune. A complete list of Tribune donors and sponsors can be viewed here.