Willingham was executed in 2004 for murdering his children via arson. Perry, as governor, signed off on the execution, despite evidence that the arson probe was flawed.
The governor has been under fire in recent days for replacing members of a state panel looking into the case. The panel's former chair, Sam Bassett, has said Perry's lawyers pressured him over the direction of the inquiry.
Perry yesterday dismissed the controversy over the panel, calling it a "sideshow." And he said that a recent report by a nationally known arson expert, calling into question the arson investigation, was being used as "propaganda" by death penalty opponents.
Perry's rivals for the GOP nomination, including Sen. Kay Bailey Hutchison, have accused him of a cover-up in removing the panel members.