Should I negotiate my severance? - what worked for you?

I was offered 12 weeks of severance after 12 years as a logistics coordinator, and I have a few days to sign. I am in Omaha, in case local advice matters. It includes health coverage for a couple of months. Did anyone negotiate and succeed?

Thanks for writing this out. I went through something close to it last year, and it got easier once I kept a simple log of every call and form.