I usually scan and load trucks to help with the tracking situation for customers like yourself. I have a feeling when you do receive your package you'll notice that the "Basic" barcode will be worn and therefore unscanable. When a package becomes unscanable an employee is supposed to manually enter the code, this can become a long and tedious process and is done on a person by person basis, but is supposedly required to be done. I have a feeling this is why you've been unable to track this package.
I'm sorry for what you're going for right now. It seems a little unprofessional for a supervisor to make a reference to someone within the company as a liar. Seems more like he might have been placating you to get off the phone.
Personally I have no idea when your package will be delivered I just know that we are so backed up right now everywhere due to holiday and compacted by weather.
I'm sure you realize that the timing of your time sensitive package was poor, and that this is not the norm. I believe that the supervisors and staff are under much duress to get customers satisfied asap, and maybe this led to poor wording on the supervisors part. I am sure your package is not actually "lost" just a little backed up and probably unscanable.
Good luck with your package. Sorry I can't be more helpful.