I previously asked this myself as well. But I just don't see it a Democrat being elected statwide in 2006. Maybe the race would have been within single digits, but Perry would have pulled it off by at least seven points or so.
The country was less polarized then though , and Democrats won the gubernatorial race in Oklahoma in not only 2006 but 2002 as well and Oklahoma even then was more Republican than Texas. Though they would need someone like Chet Edwards to pull it off and if it was a tossup George W Bush would probably go all in making sure TX stays Republican as while W Bush was unpopular nationally he was still very popular in TX.
Though the pathway to victory would have to resemble Ann Richards 1990 win more than the modern dem party pathway to winning in Texas