A Texas man whose execution was halted after lawmakers ordered him to appear at the state Capitol did not show up as planned Monday after a dispute over transporting a person on death row for the extraordinary purpose of testifying in a public hearing.Robert Roberson's absence at a highly anticipated hearing at the Texas Capitol was another twist in last-ditch efforts to spare his life over claims that outdated science and faulty evidence led to his 2003 conviction in the death of his 2-year-old daughter.It also opened tensions between a group of Republican and Democratic lawmakers who say Roberson is innocent and state Republican leaders, including Republican Gov. Greg Abbott, who say the unusual maneuver by legislators to subpoena Roberson at the last minute in an attempt to buy more time crossed a line.Roberson had been set last Thursday to become the first person in the U.S. executed over a murder conviction connected to a diagnosis of shaken baby syndrome. He was taken to America's busiest death chamber and was waiting in a holding cell when the Texas Supreme Court abruptly halted plans to give him a lethal injection.Democratic state Rep. Joe Moody, the chairman of a state House committee that led efforts to stop the execution, said as Monday's hearing opened that Roberson likely would not appear but that lawmakers still hoped he would do so soon.RELATED STORY | Texas Supreme Court pauses Robert Roberson's execution in 'shaken baby' caseIf this committee wanted to take a heavy-handed approach, there are dramatic ways that we could enforce that subpoena, Moody said. But we didn't issue the subpoena to create a constitutional crisis, and we aren't interested in creating division between branches of government.The Texas Attorney General's Office had told lawmakers that Roberson would only appear by videoconference, which Moody said would be poorly suited for Roberson because he is autistic.That doesnt mean Robert wont testify at all, said Moody, without saying when Roberson might testify or how.Among those testifying Monday about Robersons case was daytime television psychologist Dr. Phil McGraw and best-selling author John Grisham. The veteran talk show host McGraw threw his full support behind Roberson, stating that there was not enough evidence to convict him of a crime.If you execute people when you now know better, you need to abolish the death penalty. If that's the standard by which you're gonna execute people, you've got a bad system, McGraw said.Roberson's claims of innocence are backed by a group of Republican and Democratic legislators who say he was convicted based on outdated science.Roberson received the death penalty for the 2002 death of daughter Nikki Curtis in the East Texas city of Palestine. Prosecutors argued that the infants death was caused by serious head trauma from being violently shaken back and forth. Robersons attorneys say that the bruising on Curtis body was likely due to complications with severe pneumonia and not child abuse.Once Roberson testifies to lawmakers, prosecutors could seek a new execution date at any time, according to Gretchen Sween, one of his attorneys.Lawmakers had sought to have Roberson transported from death row to appear in person, raising the possibility of an extraordinary scene in the Texas Capitol. However, the state attorney general's office told the committee he would appear virtually.Abbott's office said the Texas Supreme Court should toss out the subpoena, writing that the House committee has stepped out of line in their first public statement on the case.Almost 90 lawmakers across party lines, medical experts and civil rights advocates had called on Abbott to stay his execution. Abbott has not commented on Robersons case and the Texas parole board rejected pleas to grant clemency.Rebuffed by the courts and Texas parole board in their efforts to spare Robersons life, legislators last Thursday subpoenaed Roberson to testify. Lawmakers on the House committee have expressed frustration with Texas' junk science law, which they say has failed to work as intended, including in Roberson's case.The 2013 law allows a person convicted of a crime to seek relief if the evidence used against them is no longer credible. At the time, it was hailed by the Legislature as a uniquely future-proof solution to wrongful convictions based on faulty science. But Robersons supporters say his case points to faults in the judicial system where the law has been weakened by deliberate misinterpretation from the states highest criminal court.In the last 10 years, 74 applications have been filed and ruled on under the junk science law. A third of applications were submitted by people facing the death penalty. All of them were unsuccessful.Anderson County District Attorney Allyson Mitchell, whose office prosecuted Roberson, has previously told the committee that a court hearing was held in 2022 in which Robersons attorneys presented their new evidence to a judge, who rejected their claims.RELATED STORY | Texas intends to execute Robert Roberson, whose attorneys claim he was wrongly convicted