Such a number needs 64 bits, NSInteger does only cover 32 bits (and with positive numbers only 31 bits). Try using long long values:
NSLog(@"The ID: %lld", [[user objectForKey:@"id"] longLongValue]);
you can use also NSNumber if you need to store it as an object somehow:
NSNumber *number=[NSNumber numberWithLongLong:[user[@"id"] longLongValue]];