Employment Law Questions? Ask an Employment Lawyer.
Unfortunately, severance is not legally required in your state or any other state following termination. For you to be in a position to legally compel the employer to give severance, you'd either have to be able to point to a contractual or policy requirement for the employer to give severance to everyone or you'd have to have a basis for suit. I'll touch on both areas more below.
First, for the contractual or policy piece. You'd have to have some sort of contract of employment with the company stating that you were guaranteed severance on termination. Absent that sort of contract, there are ways an employer can create a quasi contract through written company policy, which clearly indicates a right to severance. Finally, the employer can create a contractual or quasi contractual requirement by their actions. If they have given everyone severance and you are the first person they won't, then you could claim discriminatory treatment.
Second, you'd need to have some sort of legitimate threat of a lawsuit against the employer based on wrongful termination in violation of your employment contract or based on race, religion, gender, age, disability or recent FMLA discrimination. The point is that, only with the threat of a lawsuit do you have the negotiation leverage to actually convince an employer to give severance in return for your decision not to sue them.