I'm sure certain types of sociopaths do indeed support the death penalty, in fact, I'm sure some of those individuals wouldn't mind taking part in an application of it.
But I think it's better to tackle the root cause of any of these issues- no matter how much the social norm they may be and resort to such only when we have exhausted all other options, no, this ain't 'liberal drivel', I just prefer prevention over cure. It's not a case about not having enough money to do so. Killing people out of anger is dumb. As dumb and primitive as those who apparently deserve to be killed.
Death penalty or not, I do not believe that any sentient creature deserves to suffer- no matter how much of a twat they may be. I think the death penalty can only be justified as a preventative measure of the very last resort.
And I hate all that bull about lack of funding for any of option other than the death penaltly, if those politicians and various other people in 'high places' would cut down on their 'big bonusus' and petty wars, why I'm sure we could scrape together enough funds to make the world just a slightly better place for everyone regardless of what situation they're in. No sane person can deny that.
Regardless of preventative measures there will always be a few horrible individuals around, but as an agnostic athiest I cannot condone destroying life if there are other avenues to be explored.
It would make me a bad person too, no matter how accepted, because what deserves the death penalty is a subjective issue.
Edit: And public executions? Yuck! I wouldn't want to associate with anybody who enjoys watching public executions. Goodness, who knows what they'd be capable of if they'd been socialised into alternative norms and values. It's scary to think about.