NICS is Federal. The way the system works is that they run your name through the database to see of they get any initial hits. If you come up clean they approve the transfer. If you're already in the Federal computers as a Very Bad Man they immediately deny you. Any other hits and they delay the transfer pending further investigation.
The deeper investigation can be caused by an arrest record coming up showing that you've been charged with a disqualifying offense. The folks who man the system then have to check the disposition of these charges. If the state/county/whatever records are fully automated then the deeper check can take all the time of a few keystrokes. If this isn't the case, you can be delayed for up to three business days. After that period of time the FFL can release the weapon to you even if the ATF has failed to get back to him. This can happen for any number of reasons, but they say the most common is that local authorities have failed to provide the Feds with the requested information. This does occasionally lead to guns being sold to disqualified individuals, but when that happens phonecalls are made and warrants are served.
With NJ govt being shut down any NICS check that gets referred to state authorities will likely be delayed. Nobody's driving. However, this is NOT a failure of the NICS database itself and should not effect the three day rule. What it could effect is any mandatory state background checks or waiting periods. Here in MD long gun transfers are checked via NICS while handgun and EBR sales are investigated by the State Police. If this is the case in NJ, that could explain the delay and it can also lengthen your wait time. The three day rule does not apply to state systems that call for a longer investigational period.
As an aside, the NICS system gets weird and secret-policey sometimes. I've met guys with no criminal records who uniformly get delayed for the full three days and have to wait for the check to time out before they can buy weapons. The thing they all have in common is a history of involvement with fringe political activism. Nice, eh?
