"I think it's most likely that we will have that issue before the court toward the end of the current term," she said.
The 1996 law has been declared unconstitutional by a federal judge in New York and is awaiting arguments before the 2nd U.S. Circuit Court of Appeals. Those oral arguments are scheduled for Sept. 27.
The law was passed by Congress and signed by President Bill Clinton after the Hawaii Supreme Court issued a ruling in 1993 making it appear Hawaii might legalize gay marriage.
Since then, many states have banned gay marriage, while eight states have approved it, led by Massachusetts in 2004 and continuing with Connecticut, New York, Iowa, New Hampshire, Vermont, Maryland and Washington state. Maryland and Washington's laws aren't yet in effect and might be subject to referendums.
In February 2011, President Barack Obama and Attorney General Eric Holder instructed the Department of Justice to no longer defend the Defense of Marriage Act.
Ginsburg's remarks came at a conference sponsored by the University of Colorado law school. Ginsburg talked mostly about entering the legal profession when there were few female lawyers and even fewer judges.
The students roared with laughter when Ginsburg told of scrambling even to find a women's restroom in law school at Columbia University in the 1950s.
"We never complained, that's just the way it was," she said to laughter from the students.