I would be willing to bet this comes primarily from one person: George W. Bush, de facto representative to the rest of the US and the world of what a "texan" is. Despite the fact that he was born in and went to university in New England.
The rest is probably a combination of the accent and the general portrayal of the South by Hollywood. The drawl has been given the reputation that it is used by slow-minded people. I don't know why, but for some reason Hollywood has loved for decades to make southerners appear as inbred, redneck, idiots.