Whether or not you personally agree with the death penalty, and it's clear Justices Breyer and Ginsburg don't... it's an indefensible position that it is forbidden by the constitution as "cruel and unusual punishment" in the 8th amendment.
"Nor shall any person ... be deprived of life, liberty, or property, without due process of law," part of the 5th amendment, clearly implies that as long as due process of law is given, the death penalty is allowable. Furthermore, that same 5th amendment begins with "No person shall be held to answer for a capital, or otherwise infamous crime, unless on a presentment or indictment of a Grand Jury," which explicitly allows for capital punishment even more clearly.
If the death penalty is to be 100% gone, and not just de facto gone (it has been decreasing substantially), there would need to be a constitutional amendment. This language is clear. The founders and the constitution did not view capital punishment as cruel and unusual.