A Texas man who could be the first person in the U.S. executed for a murder conviction tied to a diagnosis of shaken baby syndrome is facing a lethal injection Thursday evening amid assertions by his attorneys and a diverse coalition of supporters who say he’s innocent and was convicted on faulty scientific evidence.

Robert Roberson waited to hear whether his execution might be stopped by either Texas Gov. Greg Abbott or the U.S. Supreme Court — his last two avenues for a stay. He is scheduled to receive a lethal injection at the state penitentiary in Huntsville. A Texas House committee is also trying to delay the execution by taking the extraordinary step of issuing a subpoena for Roberson to testify at a hearing next week about his case.

Roberson, 57, was condemned for the 2002 killing of his 2-year-old daughter, Nikki Curtis, in the East Texas city of Palestine. Roberson has long proclaimed his innocence, backed by some notable Republican lawmakers, Texas GOP megadonor and conservative activist Doug Deason and the lead detective on the case. Roberson’s lawyers and some medical experts say his daughter died not from abuse but from complications related to pneumonia.