Death and life without parole are the only options available to the jury that convicted Green on May 7 of raping and killing 14-year-old Abeer al-Janabi and murdering her mother, father and six-year-old sister.
Three other soldiers were given life sentences in the March 2006 atrocity devised over whiskey and a game of cards at a traffic check point in Mahmudiyah, south of Baghdad.
Green, who was named as the ringleader, was tried in civilian court after being discharged from the army due to a "personality disorder" before his role in the crime came to light.
"The victims in this case cry out for justice from their graves," assistant US attorney Brian Skared told jurors in his closing argument Wednesday morning.
Skared maintained the defense had been playing a "blame game," filling the sentencing phase with potential scapegoats who testified about Green's chaotic and neglectful childhood and shoddy leadership of his unit in Iraq in an attempt to deflect responsibility away from Green.
"They've tried to make Mr Green a victim in this case," he said.
Instead, he said Green was not acting on instinct or impulse when he killed the Janabi family but had planned the rape and murders with a "criminal and perverse mind" and then celebrated when it was over.
Skared rejected the notion that the stresses of war and losses of others in Green's unit somehow led him to commit the acts.
"If they knew their deaths were somehow being provided as mitigation for this, they would roll over in their graves," he said. "None of that explains what he did to this family."
But defense attorney Scott Wendelsdorf reminded jurors that Green had sought help for combat stress three months before killing the Janabi family, repeatedly telling a lieutenant that he wanted to kill Iraqi civilians.
Wendelsdorf said Green would not have been there to commit the crimes had he been removed from duty when he sought help.
"Steven Green was responsible (for the rape and murders) but the United States of America failed Steven Green," Wendelsdorf said.
"And it failed a lot of soldiers in Iraq. And that wouldn't amount to a hill of beans if it were not the United States of America now seeking to put Steven Green to death."
Noting that Green had never been in any serious trouble prior to this incident, Wendelsdorf urged jurors to ask themselves why Green and the other soldiers convicted of the attack on the Janabi family suddenly became criminals.
"Something happened to these men that changed them, that broke them, that crushed them and led to this '15 minutes of madness.' Whether it just broke them or whether it kills him is up to you."
In closing, Wendelsdorf pleaded with the jury to spare Green's life.
"America does not kill its broken warriors," he told them. "It does not. Spare this broken boy. For God's sake, spare him."
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