Gayland Bradford was scheduled to die by lethal injection Thursday at the state prison in Huntsville. Justice Antonin Scalia's stay will expire immediately if the court decides not to hear the case, a process that could take weeks, CNN reported.
Bradford's lawyers say he has an IQ of 68. The Supreme Court banned the execution of the mentally retarded in 2002.
Bradford was convicted and sentenced to death in 1993 for killing a security guard in a Dallas convenience store.