Just wanted to share my experience.
12/27 - took class
12/28 - confirmation email for online app
Did fingerprints and submitted rest of paperwork by the 30th.
Tried calling TXDOT and never got through, checked for status update online CONSTANTLY.
Monday 3/28 I sent an email to the Governors office. 3/30 received my plastic!!
My status has yet to be updated online. 
My husband got all his paperwork in about a week after I did. Emailed the Gov as well on 3/28 and has not received his yet. Im assuming his will be here in a few days.