Well, there have been a couple of recent examples of botched executions, which I imagine skewed things somewhat against capital punishment. That and lower crimes rates and less media emphasis on the issue of crime. If states start switching to a less accident prone form of execution than lethal injection, or if crime rates (or media panic over crime rates) rise, then I imagine support for the death penalty will go right back up.
The death penalty is little deterrent. Most who are convicted of a capital crime
(1) think themselves so clever in the commission of a crime that they will go undetected
(2) are so desperate and reckless that they don't care
(3) are stupid enough to take a loaded gun to a robbery
There have been offenders who have gone from a non-capital state to a capital-punishment state and committed a capital crime in the capital-punishment state. Just think: cold winters were more of a deterrent to Ted Bundy, who while on the lam went from Michigan to Florida.
If the death penalty were a real deterrent we would see evidence of it in warnings. Just think: A state with the death penalty could post warnings "For your safety, XXX has the death penalty for first-degree murder, perhaps with a depiction of the apparatus of execution" on highways crossing state lines, at airports and bus terminals, tail stations, seaports, and even yacht clubs (in case one of the social elite visiting from out-of-state should be thinking of committing an armed robbery at a liquor store with the possibility of shooting someone there).
Sure, there are people convicted of capital murders and subsequently executed who have college education or have been somewhat successful in business -- but the bulk seem to be toward the low end in formal education and vocational achievement.