From an AP story on a North Carolina poll (emphasis added):

The poll found that 58 percent of adults support the death penalty, but only 48 percent said it's always the most appropriate punishment for those convicted of first-degree murder, according to researchers at Elon University.

Imagine that. Only a shade less than half support a death penalty law vastly more severe than the present law, under which only a small fraction of the most heinous murderers are sentenced to death.

The actual poll is here. "It depends," the answer that reflects the law actually in controversy, is a "volunteered" answer, yet over 10 percent gave it. In polling, the number who actually favor a position is greater than the number who volunteer that option when it is not given. This is a very badly done poll.