I think most Americans don't realize how expensive the death penalty is, and IME when you explain it to them, their response is usually something like, "Well they should just shoot them, bullets are cheap." People are more inclined to see the expense of the death penalty as government inefficiency that needs to be fixed, rather than a reason to get rid of it.
In other words,
Surely there's more to it than most Americans just being blood thirsty monsters, right?
No.