Long on Monday took an overdose of prescription drugs and was being cared for at a Galveston prison hospital before being moved late today to Huntsville.
The U.S. Supreme Court refused to block the execution.
Long was condemned for the 1986 killing of three women -- with a hatchet -- at a home in Lancaster. The victims were Donna Jester, her blind cousin Dalpha Jester and Laura Owens.
He was the 32nd Texas inmate to be executed this year and the first of four scheduled to die in the next eight days. Another execution was set for Thursday.
Court rulings have determined an inmate must be aware of his surroundings and know why he is being punished before he can be executed.
Long was found "unresponsive in his cell" on death row at the Ellis Unit northeast of Huntsville, Texas Department of Criminal Justice spokesman Larry Fitzgerald said Tuesday. After treatment at the unit infirmary and Huntsville Memorial Hospital, Long was transferred to the prison system's hospital at the University of Texas Medical Branch at Galveston, where he was placed in intensive care.
"Apparently he overmedicated himself," Fitzgerald said.
Long was given prescribed anti-depressants. Fitzgerald said while the dispensing procedure is common, medical staff or officers are supposed to make certain the inmate swallows the drug.
"It would appear he hoarded medication," Fitzgerald said. "It's fair to say internal affairs will be looking into it."
It's not the first time Texas prison officials have been faced with an ill inmate on the verge of execution. In 1991, condemned murderer Jerry Joe Bird was hospitalized for treatment of a stroke in the days before he was to be executed. He was released from the Galveston hospital, returned to Huntsville and received lethal injection as scheduled.