when I lived in NJ ( Union County) my town required a permit for sheds as well. I seem to remember the main requirement was it was set back at least 5' from all property lines.
More than likely it will be a non-issue, but if they do come knocking on your door I'd be willing to bet that you'll get so many days to correct the problem and get a permit, after which time there will be a fine that will be charged for each day you are in violation
Those who can, do...
Those who can't criticize on the internet
At that point I would have to apply for a variance and hope it goes through, which I'm pretty confident it would. Just don't have 2 months to wait to apply for one right now, and don't feel like spending $1,000+ if I don't have to.