DENVER — For jurors weighing the fate of the man who killed 12 people in a Colorado movie theater, guilt may have been the easy part. It took less than two days of deliberation before they rejected defense arguments that the gunman, James E. Holmes, was legally insane when he carried out the 2012 shooting rampage.

On Wednesday, the jury of nine women and three men began considering what legal experts say is a more vexing question: Does a mentally ill defendant who carefully planned and committed such a horrific act deserve to be executed?

Prosecutors began making their case that he does. Rich Orman, a senior deputy district attorney, described the ways the crime was especially grievous: In addition to killing 12 people, Mr. Holmes had created a grave risk of death for scores of others, Mr. Orman said. He intentionally killed a child, acted in a way that was “especially heinous, cruel or depraved,” and lay in wait before attacking an unsuspecting crowd of strangers.

“They were unaware of any danger,” Mr. Orman said. “How could they be aware of any danger? They were watching a movie in a movie theater, a place of enjoyment and safety. And they were helpless.”