I've thought of a couple initial ideas.
1) OCD Guy
Incorporating Alan's suggestion of using a message from today and slotting it into the 50's, I thought of advertising a consumerism.
My idea is of a guy (character) being bombarded with products which he feels he has to buy because he fears everything and has OCD.
For example, Turtle Umbrellas (A turtle shell on a frame that rests on your shoulders). Turtle umbrellas protect your hair from radioactive fallout so even in these tough times those women can't resist your lovely full bodies locks. The other great thing about Turtle umbrellas, they protect your brain from those pesky aliens trying to send signals to your mind to control your kinetic energy and motor muscles.
A bunch of completely ridiculous products with the guy getting more and more stressed out as the awareness of the danger he is in at every angle becomes apparent to him.... to the point he has all this stuff to stop these things happening to him.... He has a Heart-Attack / Stroke and dies.
2) Burt (Off Camera)
Burt the turtle from the Duck & Cover film. Something similar to the OCD guy but the followup to the Duck & Cover film where it shows the represented character from the Federal Civil Defence Unit and how his 'alertness' in the video actually causes him problems in his real life. He could turn alcoholic of screen and something like 'destroy himself from the inside so it doesn't matter how he protected himself on the outside'.
The underside to trying to show the 'perfect American way'.