Don't forget that those minimum-wage workers pay one of the highest state/local tax rates in the nation for their income level: Texas taxes its poorest quintile 12.6% of their meagre incomes through its various taxes, the 6th-highest rate in the nation. http://www.washingtonpost.com/blogs/govbeat/wp/2013/09/21/th...
Still, even after taxes, a minimum wage salary probably goes a lot farther in Texas than in a place like NYC or SF, where the cost of living is much higher. And having even a minimum wage job puts you a lot closer to getting a higher-paid job than being on welfare, since it gives you a work history and references.
That's why I've never been a fan of sales taxes over income taxes. Texas, and the other states listed in that piece, don't have an income tax but instead rely on a sales tax and excise taxes (alcohol, tobacco, and gas) for revenues, which are all very regressive.
But an income tax is seen as a creeping evil, perpetually siphoning money away from the pockets of the citizens who worked and toiled for that hard-earned dollar. Instead, a sales tax fits more with the public's idea of a "fair" tax because it's like a "user fee," you only pay it if you use it. Don't want to pay sales tax? Easy, have Internet access and dodge it by ordering online, or just don't buy something. Don't want to pay income tax? Die.
As someone who grew up in Texas, now lives in NY, just from my observations, I think the lower-middle classes live far better and seem to be less marginalized than they are in the NY area. Home ownership is very much a possibility even on a $30k income near the population centers of Texas.