Layoff notice, what does the 60 days mean? (update)

My employer announced that the site will close and gave us written notice. It has been weighing on me all week. I do not know if I should start looking now or wait for severance news. Should I stay for the bonus?

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.