Lydia Saad reports for Gallup:

Americans' support for the death penalty as punishment for murder has plateaued in the low 60s in recent years, after several years in which support was diminishing. Sixty-three percent now favor the death penalty as the punishment for murder, similar to 61% in 2011 and 64% in 2010.

The "diminishing" is relative to the all-time high in 1994.  Almost any quantity one cares to measure is "down" if the all-time high is chosen as reference point. "Americans' support for the death penalty has varied widely over the 77 years Gallup has measured it, and now stands at 63%, which is about average for the full trend."

The death penalty retains majority support across all party identifications, all age brackets, both sexes, all regions, and all education levels.  A majority of self-identified conservatives and moderates support it, with a slight edge for opponents among liberals.  On racial lines, Gallup gives numbers only for "whites" and "nonwhites," which is not particularly helpful given that opposition has generally been stronger among blacks than other minorities.

Saad concludes, "The future course of public support for the death penalty may depend as much on the impact of unforeseen tragedies such as the Oklahoma City bombing or Newtown shootings, as it does on political campaigns by death penalty supporters and opponents. However, for now, views appear to be at a standstill, with just over six in 10 Americans in favor, essentially unchanged since 2010."