According to the FBI itself, the program -- officially known as the Next Generation Identification system -- would be charged with facial mapping mug shots currently in their system "to see if [they could] find bad guys by matching pictures with mug shots." Unless you're a criminal, that's a tough plan to argue with, except that it wasn't the whole truth. Gasp!
An investigation by the Electronic Frontier Foundation revealed that the database would actually not just include criminals, but law-abiding citizens with no criminal history whatsoever as well. People who hold jobs of any kind that require them to submit a photo as part of a background check would end up in the database too.
Of course, there is absolutely zero evidence connecting Snapchat with the FBI in any way, shape, or form, nor any to suggest that Snapchat has reason to help build out the Next Generation Identification system, because surely, Snapchat's $150 million acquisition of facial-recognition technology has nothing to do with the government. Per Snapchat's own Terms of Service, the company makes it very clear that they delete the photos and videos you send after it's viewed by the other party. They're not sharing it with any third parties or logging it into some secret database, or whatever.