The Supreme Court handed down major victories for gay marriage. The Post’s Robert Barnes breaks down the DOMA and Proposition 8 decisions from the courthouse steps. (The Fold/The Washington Post)

Big questions remained unanswered for many same-sex couples across the country Wednesday, even after the gay rights advocates responded with jubilation to the Supreme Court’s 5 to 4 decision overturning a key element of the federal Defense of Marriage Act.

Thousands of couples living in states that do not recognize gay marriage do not know yet whether they will be allowed to file their federal income taxes jointly. They also don’t know whether they are entitled to a range of marital tax exemptions, such as the estate tax provision at issue in the case that prompted the ruling.

That’s because the Internal Revenue Service, like many other federal agencies, defines marriage based on where a couple lives and not on where they married.

As a result, although the DOMA ruling grants full federal benefits to a gay couple living in Maryland, where same-sex marriage is now legal, it does not immediately grant full benefits to a couple living in Virginia, where gay marriage is not recognized.

Gay-rights supporters were quick Wednesday to press President Obama to address that inconsistency through executive action or other means.

Activists from the Human Rights Campaign and other gay-rights groups have proposed that Obama issue an order that all federal agencies define marriage based on the “place of celebration.”

Obama and his top aides, meanwhile, asked for patience, telling activists in a phone call within hours of the ruling that it will be complicated to figure out how to reinterpret or revise the hundreds of federal agency provisions affecting benefits for gay couples across the country.

Administration officials, requesting anonymity to discuss internal deliberations, said White House lawyers and Justice Department officials had begun analyzing all the relevant laws with an eye toward swift action.

Yet, these officials said, the administration was confronting complex questions that require careful consideration to avoid future legal battles. Losing such battles, they added, could prove counterproductive to gay rights.

Some conservative leaders have already threatened to sue if Obama uses his authority to issue what evangelical organizer Gary Bauer called a “de facto redefinition of marriage in states who through their democratic processes have made it clear they oppose such a change.”

Some issues are relatively clear-cut, according to people familiar with the administration’s deliberations, because a number of agencies already define marriage based on where the wedding took place.

That is true for immigration matters. As a result, the court ruling defuses an emotional question that has been part of the debate over immigration policy raging in Congress. Once the ruling takes effect, legally married gays who live anywhere in the United States should be permitted to apply for green cards for their spouses.

The Pentagon also defines marriage based on the place of celebration. Secretary of Defense Chuck Hagel said Wednesday that the agency “intends to make the same benefits available to all military spouses — regardless of sexual orientation — as soon as possible.” That, for instance, would give married gay couples the ability to live together in on-base housing and receive military health care.

A task force to begin assessing the ruling’s impact was created inside the Justice Department’s Office of Legal Counsel several days ago, according to people familiar with the process.

Obama’s gay supporters signaled Wednesday that they are willing to show some patience — but only to a point.

Chad Griffin, president of the Human Rights Campaign, pressed Attorney General Eric Holder on the matter during a private phone conversation Wednesday, according to people familiar with the call. Holder promised Griffin a “thorough and thoughtful process,” according to a statement from the gay-rights group.

Holder issued a separate statement Wednesday pledging that his agency would work “expeditiously” with other executive branch departments to put the court ruling into effect.