Legal Question in Employment Law in Texas

You can file the lawsuit, but you'll probably lose. In Texas, we have "employment at will" which means that you can be fired for any reason or for no reason at all. The exceptions: if you're fired for being a Jew, or a Negro, or a Croatian, or a woman, or for being over the age of 40.

The flip side of "employment at will" is that if you quit (with no notice), YOU can't be sued, even if your absence causes your employer to suffer financially.