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

My employer announced that the site will close and gave us written notice. I do not know if I should start looking now or wait for severance news. What did the workforce office offer?

Thanks for writing this out. I went through something close to it 12 months ago, and it settled down once I kept a simple log of every call and form.

Start your search early. I wish I had begun the day of the notice.