The last part of a death penalty trial, the part where the jury decides whether the defendant will live or die, is a sort of referendum on capital punishment.
A significant majority of Americans support the death penalty in the abstract, as an idea. But checking a box in a public opinion survey is not the same as voting to send a particular man to his death. In the polls that count, the ones that follow testimony and tears, jurors are increasingly rejecting the death penalty.
Details here from Adam Liptak of the New York Times.