I don't think it will be a big deal
My mom has a 19" analog tv on cable. We discussed the digital cutoff date some and she was worried UNTIL I mentioned that her cable box would still work with her existing television. She has no plans to replace this set.
This date is not going to "sneak up" on anyone - there will be a lot of discussion the closer we get to the cutoff date. A substantial percentage of the population get their programming through cable or Direct TV/Dish which will still work with the analog television sets.
Don't think this will be a big deal when it happens.