Though based on what you have told me, they do have the right to withdraw the offer, generally.  However, if you reasonably relied on their promise, and it caused you to make changes and loose money, as a result of their broken promise, you could possibly have a claim in quasi-contract for the amount you lost.  And of course if they did not give it to you for your age, and you are over 40, then that would be Age discriminationYou should document your request for the severence package by sending it from your email, then saving and printing it. 

But your Hr's comment alone is certainly not enought, and it appears you have not left your job thinking they were going to give you severence. 

Based strictly on what you said here, their is no legal recouse.  Sorry.

Sincerely,

Ryan Scott Nalley,                                                             

The Law Office of Ryan Scott Nalley

161 North Clark Street

Suite 4700

Chicago, Illinois 60601

Tel: 312.523.6128