The Houston Democrat said he wants a "security audit" of the state's 112 prison units after Arcade Joseph Comeaux Jr., a convicted sex offender, pulled a gun on guards and escaped.
Whitmire, who last year was contacted by a Death Row inmate using an illegal cell phone, said there should be a "shake up of the people who cannot get the job done."
"There has to be accountability. You just can't gamble with these dangerous individuals. The people of the Texas, the people of this country, deserve better, and we're going to demand that changes be made from the top to the bottom."
He added, "If the prison administrators cannot get the job done, we need to find some who can."
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