The delay could be indefinite. I’ve had customers get delayed indefinitely and we never got a response. Though usually a delay comes back resolved in less than a week.
But, as others have said, federal law doesn’t prohibit the dealer from transferring the firearm to you after 3 business days have elapsed, even if they haven’t received a response yet.
Here it is straight from the FBI website (remember, the ATF regulates guns but the FBI does the background checks):
https://www.fbi.gov/services/cjis/nics/a-nics-delay