SSN office has to validate the EAD-status. If they are able to do it online (i.e., if they can verify your EAD) then SSN will take the normal time. Otherwise SSN office has to send your details to INS and they have to respond back before they can assign a SSN number to you.
For my wife, this took around 3-4 months. We applied in NJ and they couldnt verify her details online. They sent it to INS and we did not hear from them for some time. After that we moved to MA and then I had to follow up with NJ office from here. NJ office asked us to go to MA office and we took all the documents to the Attleboro office. The lady there said that the SSN number has been assigned to my wife and all they have to do is send the card. We got the card after 2 weeks from that time. Total time was around 4 months. This is our experience. Yours can be different.
Good luck for the SSN.
Toughdba.
