To be sure, the Eighth Amendment does prohibit “cruel and unusual punishments,” but that just means that the death penalty can’t be applied in a particularly inhumane way (for example, vivisection).
Moreover, debates over the death penalty almost always occur in the context of state criminal law, over which the federal government has little authority. Yes, there’s a federal criminal code—much of which is itself of dubious constitutional authority given the outlandish reading courts have given Congress’s power to regulate interstate commerce—but it imposes capital punishment exceedingly rarely (three times in the last 50 years, not counting military justice).
All the highest-profile Supreme Court cases thus force the justices to consider whether a state’s imposition of the ultimate punishment is “cruel or unusual,” not whether the death penalty is unconstitutional altogether. So if you want to abolish the death penalty, you either have to go state-by-state—18 states have done away with it, 6 since 2007—or, as Justice Stevens suggests, you have to amend the Constitution.
But just because someone, even a Supreme Court justice, concludes that the death penalty is a bad idea, or immoral, or otherwise inappropriate, doesn’t make it unconstitutional. There can certainly be bad policies that are constitutional—or, for that matter, good policies that are unconstitutional.
Indeed, given that it’s my wont to label legislation and government action as unconstitutional, I’m frequently asked if there are any policies I like that I nevertheless think violate our founding charter. It’s a hard question, given that the Constitution is fundamentally a classical liberal, or libertarian, document, which fits with my political philosophy. Nevertheless, my top two examples are environmental regulation—properly conceived; it’s inefficient to have a tort-law based system of regulating pollution that crosses state lines—and federal tort reform.
But regardless of my personal views, too many commentators conflate that with which they agree with that which the constitution requires. Justice Stevens, even if he errs in his understanding of the right to armed self-defense and shouldn’t be proposing amendments, gets that right.