The strategy for doing so, and why it is wrong, is revealed in this article from the New York Times.

An excerpt.

Here’s the current constitutional strategy to ban capital punishment under the Eighth Amendment: Persuade the United States Supreme Court that society’s ”evolving standards of decency” have culminated in a national consensus opposing the death penalty. Point to a uniform direction of change: Six states have recently abolished capital punishment; none have newly adopted it. Opinion polls show a drop in public support, confirmed by a declining number of death sentences issued and carried out. Point out that European democracies that “share our values” have eliminated their death penalty. (Ignore the fact that European elites banned capital punishment in the teeth of overwhelming public support for it that continues to this day.) Meanwhile press state legislatures to appoint abolitionist “study commissions,” then follow their pre-ordained recommendations, until fewer than 25 states retain death as punishment. By that point, a fifth newly appointed justice will join the current abolitionist four, and a bare majority may rule that “decency” has truly “evolved” to the point where a genuine American “consensus” now exists that a punishment of death violates human dignity and thus also the Eighth Amendment.

That’s their dream, their plan, their scheme.

It might succeed, though based on false premises and misperception. When pollsters seek the appropriate punishment for the worst of the worst – a man who rapes and tortures a child, a serial killer, a depraved mass murderer such as Timothy McVeigh, etc. – overwhelmingly the people choose death as deserved. Many who prefer life without parole wrongly imagine that sadistic or callous killers experience prison as a daily punishment worse than death. My thousands of hours inside maximum-security prisons these past 30 years contradict this: Inside prison, prisoners and officers alike reject punishment.

Retrieved April 8, 2014 from http://www.nytimes.com/roomfordebate/2014/04/06/what-it-means-if-the-death-penalty-is-dying/the-death-penalty-needs-to-be-an-option-for-punishment