One of Whitaker's lawyers says if Abbott does nothing, Whitaker will be executed.
All seven members of the Texas Board of Pardons and Paroles suggested on Tuesday that Abbott change Whitaker's death sentence to life in prison based on his clemency petition, which included pleadings for mercy from Whitaker's father, who was also shot in the 2003 attack, and fellow death row inmates.
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He began to cry when the board announced that it agreed the man should not be sentenced to death.
The first execution is due to take place in Florida at 6pm local time (11pm GMT).
In a clemency petition, his father said if the death penalty were implemented, it would make his pain worse.
The gunman, Chris Brashear, pleaded guilty in 2007 to a murder charge and was sentenced to life in prison.
Whitaker had planned the murders long in advance, and it was at least his third attempt at killing his family.
Whitaker's father, Kent, also was shot but survived and has led the effort to save his 38-year-old son from execution. "They would be horrified at what's happening", Whitaker said.
Fred Felcman, the original prosecutor in the case, said the board made its decision purely because of the father's forgiveness and disregarded the large number of others affected by the murders.
Abbott said he had taken into consideration the fact that "the person who fired the gun that killed the victims did not receive the death penalty, but Mr Whitaker, who did not fire the gun, did get the death penalty".
One juror in Whitaker's case anonymously told the Houston Chronicle Wednesday that since Whitaker had convinced his roommate to carry out the murders for him, "the only way people are safe is if he's dead".
Kent Whitaker said his son has been a model inmate and has provided letters from death row prison guards to back him up. The crime deserves severe punishment for the criminals who killed them.
"The board did the hard work of examining how the offender has conducted himself since then and what impact his execution would have on the surviving victim, his father, who's already lost his wife and other son", Moody said.
The following statement was just issued from the Governor's office:"As a former trial court judge, Texas Supreme Court Justice and Attorney General involved in prosecuting some of the most notorious criminals in Texas, I have the utmost regard for the role that juries and judges play in our legal system". By all appearances, the execution looked as if it would go forward.
It's only the fourth time since the state resumed executions in 1982 that the parole board has recommended clemency this close to an inmate's scheduled execution.
Governor Greg Abbott can either approve the parole board's decision or grant a 30-day reprieve to review the case.
If the execution had proceeded, Kent Whitaker had planned to attend the execution.
The U.S. Supreme Court past year refused to review appeals in Whitaker's case.