In NJ usually the contract is written by YOUR agent, with your input, so you can really choose whatever time frame you would like. Typically the closing date is written into the contract for 60 to 90 days from the day you make the offer. It is always "on or before" a particular date. (Recently I had a sale that, per original contract, was supposed to close on April 28 and it closed last week...with both the seller and buyers agreement to the change)
For a short sale purchase it gets a bit tricky. I have put a 90 day close date, and waited another 1 to 2 months to close because it took the bank quite a while to approve the short sale.
In either case, if you work with a qualified Real Estate agent, he/she can guide you through the process and explain it in detail.
If you have not already made an offer or are not working with an agent, I would be happy to help you and explain it myself.