I was over in JFK the last two days - complete zoo. On Saturday, many, many airplanes diverted from JFK to Albany, Dulles, Philly, and Hartford. Personally, it took me 9 hours to commute from DTW-JFK: long story short, it ended with a bus from ALB-JFK.
For me, scheduling was mostly on the ball. I think they were just completely overwhelmed. When one of your big, international hubs has most of the planes divert and dozens of planes on the ground there cancel - things aren't going run smoothly. I think the sheer number of changes would make it hard for them to call everyone.
Which is why the IT department needs to use some technology! I mean - how hard is it to have the automated call system be programmed to call pilots who's schedules have changed to say, "This is Delta Pilot crew scheduling - your rotation NYC1234 has changed/cancelled/ etc. Please check your schedule via iCrew/the VRU. Please only call scheduling if you cannot check your schedule online because we are really swamped".
Or they could send it via text message (to those who sign up in DBMS for that - so that we don't have to pay for a text if we don't have it on our.
phone).