That and a willingness to ignore fundamental tenets of due process. I suspect that if anyone of the "fewer appeals" crowd had a loved one who was up for capital murder with a claim of innocence, they'd be all about more appeals and careful examination of what's going on.
I'm honestly against the death penalty in every cir stance. It is not my place to deprive any person of his life, regardless of the reasons for suggesting that he should die. There is value in every person, even if that person commits acts that we might deem unpardonable. A life behind bars remains a life open to the possibility of making atonement and seeking foregiveness. Even if its a remote possiblity, it's a possibility. Plus, in most cases, we can't be 100% sure that the convicted person actually committed the murder -- there have been too many instances in which people sentenced to death were later shown to be innocent for me to believe that death sentences accurately reflect what took place.