This is also Texas:
Get T-Boone to build windmills to do the pumping.
If you started up near Dallas and dug straight down about 500 feet, you could then proceed at that same depth toward the Gulf Coast (stopping by Austin first and then over past Houston).
Of course, you'd have to pave the entire length of the thing to keep that arid land from sucking the channel dry at anything less than high tide. And you'd have to put some big-ass flood gates in at the mouth of the thing, lest several inland Texas cities end up getting hurricane storm surge. :-)
It would sure put the "Big Dig" to shame. But talk about your shovel-ready jobs!