Unsure of that, Party affiliation in TX is not a simple equation. There were no Republicans in TX in my youth, and it only became common after the Left totally took over the Dem Party in early 1970's. A carry-over from what helped populated the state originally. CW1
I simply do not think Medina is sufficiently defined on her own at this point to overcome the negative of the Republican label in some parts of the state. I know some good people (poorly informed) who will never as long as they draw breath vote for a Republican. Most of those people refused to vote for Obozo.
As far as Bill White, I am not sure about his following.
Thank you for your analysis, it confirms what I have been told about Texas and their political leanings and history