Illinois was my first full license. Once I had all of the paperwork submitted, it only took them a few weeks to receive the license. The harder part was that for my state controlled substance number they wanted an Illinois address. I used the hospital's address, which was a mistake, because the hospital would not keep track of things like that. To get the hospital privileges approved, I drove up to Springfield, spoke with the people in the office (who were very friendly and helpful), and they gave me a physical copy of my documents, which I then sent onto the hospital. I still think my original copy is floating around somewhere in the hospital's ether.
My Utah license did not take too long, once I had all of the information together, just a few weeks
My most recent license in Washington state took a while. In this case both FSMB and waiting for Illinois to send verification were the holdups. Once they had all the information, they approved it a few days later.
Hospital credentialing is far worse than obtaining a license. My experience with credentialing is that Illinois and Washington are about the same in terms of difficulty. Once you gather all of the information and submit it, the longest wait is for your peer references and previous hospitals to send their reports.