@zeePa -- waiting is normal but waiting while you have valid i797 is unusual. I had to go through waiting twice in 6 months.
There are 3 steps in verification while you go to DMV. In the 1st step DMV people put your info in their website which has direct link to USCIS. If they can verify they will issue based on your current status expiration. If they cannot veirfy they will send your info to state HQ (In case of Texas they will send to Austin). Infact In my case I had to call Austin few times. If your state HQ can verify your info they will update in their system and send you a letter and will ask you to go back to DMV with that letter. 5-7 business days. If Austin cannot verify your current immigration status, they will forward the case to USICS and ask them to verify\update. This takes about 21 business days. In this case you will still receive letter. ANd you can go back to DMV with that letter.
IN my case I had to wait twice. The last one I drove without license for few weeks and a letter and form from DMV so that if I get pulled over I can show them my paperwork.
The issue here is that your recent i-94 fromH1-B has not been updated in DMV websites.
Hope this helps..