Justices have repeatedly refused to revisit issues raised by their 1980 decision that banned the posting of copies of the Ten Commandments in public school classrooms.
CBS News Legal Analyst Andrew Cohen points out that this is not the case involving, who lost his job for defying a court order to remove a Ten Commandments monument from his courthouse. The justices rejected an appeal from Moore last week.
"I don't think the justices took this case to ride to the rescue of Judge Roy Moore," says Cohen. "If they had wanted to do that they could have taken the appeal he brought and they didn't. I think the court took the case because lower federal courts have issued too many different rulings based upon too many differing legal theories of the first amendment and its application to these sorts of cases."
But, Cohen adds, "obviously the decision in this case relates to the issues Judge Moore raised with the placement of his commandments. And if the court sides with his view of the first amendment, his religious monument could come back into that public building."
Lower courts have reached a hodgepodge of conflicting rulings that allow displays in some instances but not in others.
The high court will hear an appeal early next year involving displays in Kentucky and Texas.
In the Texas case, the justices will decide if a Ten Commandments monument on the state Capitol grounds is an unconstitutional attempt to establish state-sponsored religion.
A homeless man, Thomas Van Orden, lost his lawsuit to have the 6-foot tall red granite removed. The Fraternal Order of Eagles donated the monument to the state in 1961. The group gave scores of similar monuments to American towns during the 1950s and '60s, and those have been the subject of multiple court fights.
Separately, they will consider whether a lower court wrongly barred the posting of the Ten Commandments in Kentucky courthouses.
McCreary and Pulaski county officials hung framed copies of the Ten Commandments in their courthouses and later added other documents, such as the Magna Charter and Declaration of Independence, after the display was challenged.
The Ten Commandments contain both religious and secular directives, including the familiar proscriptions on stealing, killing and adultery. The Bible says God gave the list to Moses.
The Constitution bars any state "establishment" of religion. That means the government cannot promote religion in general, or favor one faith over another.
The lawyer for the Kentucky counties, Mathew Staver of the conservative law group Liberty Counsel, told justices that lower courts are fractured on the issue. A divided appeals court panel sided with the American Civil Liberties Union in the Kentucky case.
In the past decade, justices have refused to get involved in Ten Commandments disputes from around the country. Three conservative justices complained in 2001, when the court declined to rule on the constitutionality of a Ten Commandments display in front of the Elkhart, Ind., Municipal Building.
Chief Justice William H. Rehnquist, joined by Justices Antonin Scalia and Clarence Thomas, said the city sought to reflect the cultural, historical and legal significance of the commandments. Rehnquist noted that justices' own chambers include a carving of Moses holding the Ten Commandments.
The Rev. Barry W. Lynn of Americans United for Separation of Church and State said Tuesday that he hopes the court uses the cases to declare government displays of religious documents and symbols unconstitutional.
"It's clear that the Ten Commandments is a religious document. Its display is appropriate in houses of worship but not at the seat of government," Lynn said.
The cases are Van Orden v. Perry, 03-1500 and McCreary County v. ACLU, 03-1693.
In other moves Tuesday, the Supreme Court: