These sorts of disputes have happened before, and they always get resolved, with minimal disruption to the viewers.
That is, if you consider the loss of CBS programming a major life problem in the first place...................
When I had DirecTV, they sometimes would take too long to resolve. I am with ATT/DTV now, so I think your scenario will pan out. However, I don't watch anything on CBS except some golf tournaments on the weekend.
The nastiest were the Cablevision disputes with various program providers. It wasn’t until it was bought by Altice Europe that those disputes stopped.