The U.S. Open just teed off as I write this, this year at Oakmont. The USGA has visited Oakmont eight times for the national championship - it's one of the venerable, old-money, Northeast courses the USGA loves (they also have a couple favorite in California).
A major hasn't been played in Texas since 1969. And that's not likely to change anytime soon, as the Dallas Morning News explains in this very interesting article (try bugmenot.com if you're asked for a password in order to log in).
Turns out that several DFW courses have tried, more recently than I was aware of, to get considered for U.S. Opens and PGA Championships. Without success, obviously. But making the effort is the first step.
When Dallas National was built a few years back, its ownership made no secret of the fact they wanted to bring a U.S. Open to Dallas. They found what designer Tom Fazio called "the greatest piece of land left in America close to a downtown," a dramatic property of the type preferred for majors, and Fazio set out to produce a very challenging layout that included the touches needed to host huge events (plenty of room for spectators and corporate tents, for example).
And Dallas National has talked to the USGA and PGA of America. The club will never get a U.S. Open without first hosting a smaller USGA championship (such as the Mid-Am or Junior Am), something the article says the club is reluctant to do. (Well, do you want the U.S. Open or not?)
Dallas National seems to have had more success in broaching the idea of hosting a Ryder Cup or Presidents Cup. The article says that Dallas National was a finalist to host the 2009 Presidents Cup, but eventually lost to San Francisco's Harding Park. However, "Dallas National was encouraged to apply for the 2013 Presidents Cup," the article states.
It's a good read that goes into a lot of detail about the hurdles Texas courses face in attracting a major.
Update: As a commenter pointed out, and as the DMN article points out, one of the problems Texas courses face is the weather. In the hot Texas summers it's tough to keep courses at peak condition. But greens shouldn't be a problem for many of the courses that would seek to host a major, especially newer ones. Many courses now have bentgrass greens that stay alive during the hot months only through the use of sub-air systems. Air conditioning for grass roots, basically.