4-8 weeks for license number to be issued from when you pass the NCLEX as all applications are submitted to board committee once all components are complete/received (background/fingerprints, school documents, NLCEX result, application uploaded/entered (if paper application) or online application verified, other relevant credentials, etc.) . Once your license appears on the NJBoN site (and subsequently Nursys once the update is uploaded to Nursys from NJBoN) you are a licensed nurse eligible to work as same. It can take a few days to a few weeks to receive your paper license depending on batch printing of the documents and the USPS.
I would just suggest driving to the Board of Nursing in Newark and speaking with them. I took the NCLEX on 4/13/13 and have been waiting and waiting. Everytime I call I get a different story and my classmate who took the test a few days after I did told me to just drive down there and get my license number. I did that this morning and they told me it would be online by 4pm. It was there by 11:30AM.
I was worried because a few of my other classmates recieved letters in the mail weeks ago and I got nothing. Its best to just handle it yourself. Dont even bother calling anyone on the phone because from what I experienced they dont know what they are doing.