Atwater's background and mental health is also a sticking point. His attorneys say they need to call in expert witnesses after he undergoes an evaluation.
Carson, 22, was found slain in March 2008. She was shot five times - including once in the head with a 12-gauge shotgun - and left on a street near the UNC campus.
Atwater faces 11 state and federal charges including murder, kidnapping, and carjacking resulting in death. He could get the death penalty if convicted.
Another man, Laurence Alvin Lovette Jr., 18, is also charged in the case, but will be tried separately. He will not face the death penalty because he was 17 at the time of the murder.