The court may also be asked to rule on whether former attorney general John Ashcroft can be personally held liable for excesses in arresting scores of foreigners immediately after the September 11, 2001, attacks.
Its last term was marked by a series of conservative rulings on social issues including abortion and freedom of speech relating to political campaigning.
But in the divided court, which has five conservatives and four progressive justices, major decisions in the new session could depend on Justice Anthony Kennedy -- the most pragmatic of the conservatives -- who this year may find reasons to switch camps on some cases.
The court also will have to rule on a series of other issues that might figure prominently during the election campaign.
The justices have already chosen to consider if executions by lethal injection are constitutional, if a child pornography law infringed upon the constitutional right to free expression, and if prison sentences for trafficking in crack cocaine were excessive.
The court also will examine if child rapists who did not kill their victims can be sentenced to death.
In early September, the city of Washington, DC asked the high court to rule for the first time in nearly 70 years on the Second Amendment to the constitution, which is viewed by some as a guarantee of the right of every American to own a firearm.
