I just spoke with the Illinois Department of Professional Regulation with questions regarding licensure by endorsement, and thought I would post the info here in case it is of use to others.
(I spent 1.5 hours redialing to get past the busy tone, and then spent 20 minutes on hold. But the woman who answered was friendly and helpful.)
I requested the fingerprint card, and she took down my address and said these requests are processed pretty quickly.
Typical waiting periods, once all the paperwork has arrived in their office:
4-6 weeks for a temporary permit
8-10 weeks for a permanent license
(She said that if there are any aspects of the application requiring further investigation it will add at least three weeks to the process.)
As of today (6/20) the area that handles the RN licenses is working on files from June 2nd. So they are 18 days behind.
I am in California, and I mentioned to her that the BRN here sends the form directly to Illinois instead of returning it to me, and she said that is not a problem.