HOUSTON --The hearing in a Houston courtroom over the constitutionality of the state's death penalty has been halted, but what's at stake here is really beyond John Edward Green, Jr.'s case and could set a precedent for future death penalty cases. Attorneys for Green admit Harris County, Texas, may not be the easiest place to argue the constitutionality of the death penalty. "We are at a moment where the people of this state and of this country are questioning whether we should have a death penalty, in large part because they are concerned about innocent people being convicted and put to death," said Richard Burr, Green's attorney. Less than two months ago, 45-year-old Anthony Graves of Brenham was freed after 18 years on death row. The hearing on Tuesday involved 25-year-old Green, who is charged in a 2008 robbery on the southwest side that left a man dead and his sister injured. His attorneys argue evidence in his case is the same type of evidence that has led to other wrongful convictions, from questionable forensic evidence to possible mistaken identity evidence. "Once you understand that the kind of evidence that has led to wrongful convictions of other people in capital cases is all the evidence that is going to be presented against John Green, you ought to be concerned," Burr said. The Harris County District Attorney's Office doesn't believe there is a valid legal argument in the case. On Tuesday, the Texas Court of Criminal Appeals granted a stay in the death penalty hearing, effectively stopping the pending legal arguments to be made by all parties. "The court of criminal appeals sent a very strong message to this judge -- and any other judge -- that if you're gonna mess with the death penalty, we're gonna stop you," KTRK Legal Analyst Joel Androphy said. It is a case with many unusual legal twists. The hearing itself is unprecedented. Generally, the appeals court let trials courts finish work and then reviews it; and attorneys are making arguments before Green has even gone to trial. Before that trial happens, Green's attorneys are optimistic Tuesday's halted hearing will eventually continue. "We're halfway through it," said Casey Keirnan, Green's Attorney. "We've landed on the beaches of Normandy, and we are ready to go all the way in." Both sides have 15 days to state their positions. If Green's attorneys win, it will mean if convicted, Green wouldn't be eligible for the death penalty during the sentencing phase of his trial. His attorneys also add it would put a "chink in the armor" of the Texas death penalty.