The manager said there would be downsizing, and I was the first to go.

Yesterday, the boss held a meeting with us and said there would be downsizing but didn’t provide details. Later in the evening, he called me and informed me that my position was no longer necessary and that I was being terminated. I hadn't received any written notice; it all happened quite suddenly. He said we would provide severance and notice pay. Is it really that easy legally? Is it worth filing a lawsuit?