Is it some sort of Tradescantia?

Looks like small carpgrass, Arthraxon hispidus. An up and coming invasive in the Northeast. Usually in damp places, though.

I see that Arthraxon has been recorded from Texas, but just in one county. Doesn't mean much, it's just over the border in Louisiana. But I agree, this could be something in the Commelinaceae. Obviously what we need is a pic of the flower.

I have never seen a flower. I will look more closely and see if there is a small flower any where in it.

Arthraxon is in the commelinadae subclass, so I'd say it's a possibility. Are there hairs or bristles on the edges of the leaves?

No noticeable hairs or bristles. The leaves are quite smooth and it drops roots down every 3/4" or so.

I think it's one of the dayflowers; if it is, you should be seeing a blue flower any time now. Most herbicides don't work on dayflowers, which leaves hand-pulling; in my experience (& I've been fighting dayflower for years), it's much easier to pull when the ground is moist, as the stem will just break off and leave the roots if the ground is dry.

Here's the Wikipedia page on the dayflower family: https://en.wikipedia.org/wiki/Commelinaceae; if you can track down some close up pictures as good as the one you posted, maybe you can firm up the dayflower diagnosis.