As we have noted here many times, polls on the death penalty vary dramatically depending on how you ask the question.  (See here and here.)  The generic question Gallup has been asking since the 30s has generally shown about 2/3 of the people in favor of the death penalty for the last couple decades.  The worst way to ask the question, among those commonly used by pollsters, is to force the respondent to choose one penalty for all murders, or perhaps all first-degree murders, and offer the choice of death or life in prison.  That question has generally produced a roughly even split.

If that were actually the question, I would say life in prison myself, as strong an advocate of the death penalty as I am.  But of course it is not.  The actual public policy question is what penalty to impose on the worst murderers.

Public Policy Institute of California has a poll out asking the question the worst way: "Which of the following statements do you agree with more? The penalty for first-degree murder should be the death penalty; or the penalty for first degree murder should be life imprisonment with absolutely no possibility of parole."  Note "the penalty," definite article and singular noun.  Death for worst and life for the rest is not offered as an option.

They get 42% for death and 50% for LWOP among likely voters.  That's a bit of a shift from the usual.  They count 8% for "don't know."  I wonder how many actually said, "That's not the question, dummy."