When Justice Stevens retires at the end of this term, for instance, there will be no Protestants on the court. The United States is roughly 51 percent Protestant, according to a 2008 survey by the Pew Forum on Religion and Public Life.
The Supreme Court was entirely Protestant until 1836, when the first Catholic justice, Roger Taney, was appointed. In 1916, Louis Brandeis became the first Jewish justice on the Court.
"Does it matter if he puts a Catholic or a Jewish person, or someone of another faith on a court?" Clinton asked on ABC News' "This Week." last month. "There would be no Protestants on the Supreme Court. Does that matter?"
Though such questions are being raised, "In the end, I don't think that sort of thing is going to govern the choice," said National Journal's Stuart Taylor.
Another possible issue is that, with the eight remaining justices all alumni of Ivy League law schools, including seven from Harvard or Yale, some observers suggest the next nominee should come from somewhere else.
Taylor said there are more than enough Harvard and Yale alumni on the court "for sure," but perhaps a nominee's law school may not matter much.
"I'm not sure you add intellectual diversity if you take somebody from the University of Texas Law School, for example, like Judge [Diane] Wood," Stuart said. "How diverse is that after they've been out for 30 years or 20 years?"
Of the current short listers, only four are non-Ivy Leaguers -- Judge Wood, Judge Sidney Thomas, Judge Ann Claire Williams, and Homeland Security Secretary Janet Napolitano. The others -- Elena Kagan, Merrick Garland, Jennifer Granholm, Justice Leah Ward Sears and Harvard Law School Dean Martha Minow -- all have Ivy League backgrounds.
But Obama has said he would apply no "litmus test" when it comes to whether a nominee supports abortion rights, but added that he would want a nominee who would interpret the Constitution as taking into account individual rights, including women's rights.
"The bottom line is that the president is going to want to look for somebody who has the ideology he likes ... who is confirmable as he wants them to be," Taylor said. "He doesn't want a big fight. And [he'll look at] who seems like he or she would be a very good justice."