The news on Wednesday out of the Supreme Court was at least slightly better for gay-rights advocates than it had been the day before. After the oral arguments in the case of New York resident Edith Windsor, who is challenging the constitutionality of the Defense of Marriage Act, SCOTUSblog, which watches the Court carefully, predicted on Twitter that there was an eighty per cent chance that DOMA would be overturned. It appeared from the arguments that there were at least five justices who were highly skeptical that the law—which prevents the federal government from recognizing otherwise valid state-sanctioned same-sex marriages—is constitutional.

Tuesday’s historic arguments on Proposition 8 were, comparatively, a bit of a letdown for gay-rights proponents: the Justices seemed to regret taking the case, and to be far from a sweeping assertion that there was a constitutional right to marry. Many were left asking what had happened. How could it be that Theodore Olson, the Republican former Solicitor General who was arguing the case on behalf of the gay and lesbian California plaintiffs, was not able to tap into the bigness of the moment? Had he been too legally strategic? Or was he simply hamstrung by the Court’s unwillingness to engage in a larger discussion, which left the Justices instead looking for excuses not to decide the most significant civil-rights issue before the Court this term.

Whatever the outcome in the Proposition 8 case, it was a relief to many that in the DOMA case, the Court seemed fully ready to engage in a discussion of how Congress could have decided to regulate marriages, traditionally the province of state regulation, and in doing so cut out a whole group of people. What was their motivation, the Justices asked. And was that motivation permissible?

The four more liberal justices in their questioning seemed to suggest that they believed that Congress was intentionally, and impermissibly, trying to make homosexuals second-class citizens. Justice Ginsburg spoke of “skim-milk marriage.” Justice Anthony Kennedy’s swing vote seemed, at least today, to belong to gay-rights advocates. He questioned whether the federal government had the historical authority to regulate marriage, long a state-regulated institution.

While it looked as if there were probably a majority of Justices willing to overturn DOMA, the more important thing for the future will be the grounds upon which they do so. We will not know for sure until a final ruling—and there were not many clues today—whether a majority of the Court is ready to hold that any legislative classifications based upon sexual orientation are entitled to so-called heightened constitutional scrutiny. That would mean that any law that treats gay people differently than straight people would be in serious legal jeopardy.

Beyond the question of whether the plaintiff, Edith Windsor, a widow who brought the case after she paid $363,000 more in estate taxes than she would have had the government recognized her marriage to her wife, gets her money back—even beyond the question of DOMA—the question of heightened scrutiny is the most important issue in this case. If the Court articulates a new and more forward-leaning standard of review in sexual-orientation-discrimination cases, as advocates hope, it would be truly transformative—so much so that even if the Court decided not to rule in yesterday’s Proposition 8 case, anti-gay-marriage laws would soon be doomed in any future litigation.

That is not to say that the outcome, based on Wednesday’s argument, is a sure thing. There continued to be a lot of questions on the issue of standing. In this case, the question is whether the Administration has the ability to appeal from a ruling they don’t really disagree with. Also, whether Republicans in the House of Representatives had the power to step into the Justice Department’s role and defend the law once President Obama declined to do so. This is a highly unorthodox situation and, as a number of the Justices noted, one in which there is no exact precedent. No doubt, the conservative Justices will try to grab onto that argument and run with it, especially if they see five votes on the other side of the constitutionality issue.

But much more so than after Tuesday’s arguments, advocates had reason to be confident as they were leaving the Court. Edith Windsor, who is eighty-three years old, spoke to reporters on the Court’s steps, looking radiant, and said, when asked to predict the outcome, “I think it’s going to be good.” She added that it had been a “spectacular day” for her and that the spirit of her deceased wife and the love of her life, Thea Spyer, was there watching over it all. When a reporter asked her to describe a brooch she was wearing—a gift from her late wife—Windsor started to talk about the four decades she spent with Thea. Then she paused, momentarily overcome by emotion. She stopped mid-sentence, and appeared to be trying to catch her breath and hold back tears. And then she smiled—a smile of classic dignity and grace—and simply asked reporters if she might be excused to go and greet her friends and supporters. No one objected.

Richard Socarides is an attorney, political strategist, writer, and longtime gay-rights advocate. He served as White House Special Assistant and Senior Adviser during the Clinton Administration.

Edith Windsor (second from left), arrives with her attorney at the Supreme Court. Photograph by Joshua Roberts/Reuters.

[#image: /photos/5909519dc14b3c606c1038ea]Read our full coverage of gay marriage before the Supreme Court.