What if I don’t want to watch the President speak while I was trying to watch I Love Lucy? Is there something I can buy for my television that could let me watch the tv show instead of seeing these special reports I don’t care about?
You can only see what the station wants you to see.
However, an exception exists: If you’re watching national programming on a network affiliate, and the affiliate breaks in with some local news, if you have a C-band satelite dish, you can tune in directly to the network feed instead of the local station.
That would be the greatest invention in the history of television. 
Unfortunately, there’s really nothing you can do, since the Special Report is being transmitted in place of the program it’s interrupting at the TV transmitter. Short of calling the TV station and complaining (and hope that a significant fraction of the station’s viewership does likewise), there’s nothing else to be done. You can either watch it, or change channels.
They should have a list of people who would rather not know if nuclear missiles are approaching their country, and prevent them from receiving the warning. I personally would sooner just keep watching Lucy.
You could just tick a box on the census form. MASS HYSTERIA/NON MASS HYSTERIA.
A variation to Friedos post;
When I was in college, I got two CBS feeds on my TV, one was the Atlanta affiliate, the other was the North Georgia CBS affiliate. The county I was in was required to have weekly EBS (Emergency Broadcast System) tests. The annoying beep was on one CBS feed, so I swtiched to the other. Virtually the same soultion, just a different path to it.
BTW; Any other Atlanta Dopers fed up with WGCLs breaking into The Price is Right for NON breaking news?