There is a difference between endorsing it, and re-phrasing the issue so it does not appear that the life of a condemneed criminal (granted some of them might be innocent, but most are reprehensible monsters) appears to the primary concern. That creates an illusion of being more concerned about criminals than their victims.
To illustrate that with a real life example, instead of "endorsing abortion on demand" which is a controversial formulation of a broader social problem women face - the Labor Party (in the US) stated its position as "support for a full range of reproductive care services." This is tantamount to saying that they refused to address the problem as a choice between two alternatives dictated by the current system, but instead they opt for a "systemic" solution to address the root causes of the problem.
In the same vein, instead of opposing or supporting the death penalty, the issue can be formulated as a support for social and criminal justice policies that reduce crime and crime victimization, and at the same time guarantee a fair trail regardless of the economic status.
I am pretty sure is the social condition producing monsters like King or -what's the name of the recent white supremacist killer in CA? - are eliminated, the public support for capital punishment will disappear as well.
wojtek