Ideally, DPS would perform a instant background check on you, the day they receive your paperwork, check to make sure you paid your fees, and then issue your license the next day. Unfortunately, this being a bureaucracy, there are delays in the system. it takes time to get the background checks done, especially if you have any out-of-state residencies. Then, the people that filed before you are in line before you, too.
All in all, it takes a while to "process" and then print your license. The time has varied over the last few years from as short as a couple of weeks (mine, for example, took 18 days from reciept in Austin to putting the license in the mail to me) to as much as six weeks (though there are always folks that take longer). By law, once your application is complete (all of the needed documents are received at the DPS, and you've paid your fee) they have 60 days to get everything done, and that's if everything is OK. If there are things that need extra explanation from you (a disposition over an arrest, for example, or any other inconsistency in your application) the clock gets reset.
Hang in there, though. it'll get there. In the mean time, practice with your selected holster(s) around the house, and do some dry-fire exercises.
![Laughing :lol:](./images/smilies/icon_lol.gif)