The ability to lawfully kill someone is the ability no human being has the right to possess. However that is the meaning of the death sentence, the ability to kill another human free of repercussions. "Are some crimes so horrific... That any punishment short of death is simply inadequate?" No, there is no possible position in which the murder of a potentially innocent human being, no matter how heinous the crime of which they are accused, is morally justified.
However the party opposing the death penalty is on the rise. The amount of states refusing to back the murder of another human being has risen by almost one per year for the last five years. And "the number of annual executions in the U.S. has declined from 98 in 1999 to 39 in 2013." Another 11 states are close to the same conclusion. If people are being executed for the murder if others, why doesn't the death penalty apply to those administering it?
There is no activity in which we can partake that is so brutal and cruel that for it we deserve to die. A life taken is no excuse to take another. Similar to the idea that we let violence lead to more violence, we are letting death lead to more death. As a nation, by justifying the death of criminals, we are saying they killed someone and that that's illegal, why don't go ahead and kill them.