First of all, condolences. Layoffs are never easy and I hate to see they are happening even at this time of year. Generally, there's not much leverage for you to negotiate unless you they want you to sign away your rights to sue them in exchange for the severance payment. Even then, this is often a "take it or leave it" offer unless you really do have good grounds to sue them (like evidence the layoff was conducted in an illegally discriminatory fashion, or you were recently sexually harassed, etc.). If you live in the US, legally they almost always owe you nothing unless the layoff should've triggered a WARN notice, then they owe you 60 calendar days of salary (but fact check me on that). It may be possible to trade things in the package you don't want/need away for something else (e.g. instead of covering my health insurance for six months, just give me some extra cash instead; instead of paying me cash, how about you exercise some of my stock options for me). Best of luck to you in moving on from this quickly.

Thank you so much for the feedback. I wound up negotiating an extra week of pay, although I now feel the need to research the WARN notice clause you mentioned. As this has totally caught me off guard, i want to arm myself with as much info as possible.