Gallup: Percent of Americans who believe that death penalty is morally acceptable essentially unchanged since 2001

Gallup implies that support is waning.

The results are based on Gallup's annual Values and Beliefs poll, conducted May 8-11. On April 29, an Oklahoma death row inmate given a lethal injection appeared to suffer for an extended period of time until finally dying of a heart attack. That incident led to the postponement of a second execution scheduled in Oklahoma that day and raised questions about the methods used to execute prisoners. 

The case did not fundamentally alter Americans' perceptions of the death penalty, however, with a solid majority viewing it as morally acceptable. This percentage is similar to the 60% who say they favor the death penalty as punishment for murder in Gallup's October update. 

But the longer-term trends reveal that Americans have become less supportive of the death penalty. Gallup first asked the moral acceptability question in 2001, with an average 66% saying it was acceptable between 2001 and the peak in 2006. Over the last three years, the percentage saying it is morally acceptable has averaged 60%. . . .

The Gallup poll was right after Oklahoma "botched" effort.  Another Angus Reid poll showed record support after Boston Bombing. 

78 per cent of respondents (+8 since September 2011) supportthe possibility of prosecutors relying on the deathpenalty for murder cases in the United States.
The poll was conducted after the Boston Marathon bombings and concluded before the massive manhunt that resulted in the arrest of one of the suspects.
Respondents in the South (80%) and West (79%) are more likely to endorse capital punishment, along with supporters of the Republican Party (86%). . . . 

But if you look at the average since 1936, the current poll numbers are almost the same as the average from 1936 through 2012.