I don't know about the modern American Christian right.
But Christians became accustomed to the use of the death penalty fairly early on.
Saint Augustine, for example, would have been unimpressed by arguments against the death penalty based on the moral horror of accidentally killing the innocent from time to time. Here's what he had to say, in Book XIX, chapter 6 of the City of God (c. 426 AD) -- pp.926-8 of the recent Cambridge translation. Note that witnesses were in these times routinely tortured, to make sure their testimony was reliable, and defendants also:
"And when he [the accused] has been condemned and put to death, the judge does still not know whether he has slain a guilty man or an innocent one, even after torturing him to avoid ignorantly slaying the innocent. In this case he has tortured an innocent man in order to discover the truth, and has killed him while still not knowing it.
"Given that social life is surrounded by such darkness, will the wise man take his seat on the judge's bench, or will he not venture to do so? Clearly, he will take his seat, for the claims of human society, which he thinks it wicked to abandon, constrain him and draw him to his duty. He does not think it a wickedness that innocent witnesses should be tortured in cases which are not their own or that the accused are so often overcome by such great pain that they make false confessions and are punished in spite of their innocence. Nor does he think it wicked that, even if not condemned to die, they very often die under torture or as a result of torture... The philosopher does not consider that these many and grievous evils are sins; for he reflects that the wise judge does not act in this way through a wish to do harm. Rather, he does so because, on the one hand, ignorance is unavoidable, and, on the other, judgment is also unavoidable because human society compels it.
"Here, therefore, granted that it does not arise out of malice on the part of the wise judge, we certainly have an instance of what I call the wretchedness of man's condition. If it is through unavoidable ignorance and the unavoidable duty of judging that he tortures the innocent, then he himself is certainly not guilty. But is he also happy? Surely it would be more compassionate, and more worthy of the dignity of man, if he were to acknowledge that the necessity of acting in this way is a miserable one: if he hated his own part in it, and if, with the knowledge of godliness, he cried out to God, "From my necessities deliver Thou me.""
Chris Brooke voiceoftheturtle.org