So they have everything else already (i.e transcripts, ethics exam, SERs, 3 references, finger prints/criminal background check, FE verification, etc. [or this is completed:
http://engineer.texas.gov/downloads/checklist.pdf])?
I had to do all of this to get approval to sit for the exam - it took me 4-5 weeks to get to this point (and I was pressing hard to get them everything). I would guess if you get to this point you'll be issued your license.
Probably the thing that takes the longest is getting your SERs signed and sent to TBPE. Once they are sent then they are reviewed.