The good news for those who want the United States to join the company of civilized nations (nations who have eliminated the death penalty) is that support for the death penalty has been dropping for the last twenty years -- from a high of 80% in the mid-nineties to about 61% in 2015. That's a drop of about 19 points (see the chart above).
The bad news is that 61% (or about 6 out of 10 Americans) still support the death penalty -- and a plurality of 40% would like to see even more people put to death in this country (see the chart below). I'm sure most of that 61% would be happy to claim that this country is a bastion of human rights, while supporting something that puts us on a level with countries like Iran, China, North Korea, Russia, and other countries known for their lack of respect for human rights.
I find that very disturbing, and coupled with the fact that we put more people in prison than any other nation (both in raw numbers and as a percentage of our population), I think it's more than a little disingenuous to claim we are a country that respects freedom and human rights. We are not living up to the principles we claim to represent.
These charts are from a new Gallup Poll -- done between October 7th and 11th of a random national sample of 1,015 adults, with a margin of error of 4 points.