Before you answer that question, take a good luck at the photo above. That Cadillac and its perfectly-coiffed driver have lived through nuclear hell. The paint looks to be in good shape, the windows are mostly intact and the tires are even still fully inflated. A testament to 1950s Detroit iron or 1950s propaganda? Maybe a little of both.
The Caddy above and dozens of other now-classic cars you can see in the gallery below were used in the government's "Operation Doorstep" project. As part of the program, houses and cars were set up near nuclear test sites in Nevada to study the bombs' effects on people and property. What those tests showed (or at least what the public was told) is that not only could cars survive a nuclear blast surprisingly well, but they also made wonderful shelters for people.
But as a pamphlet from that era pointed out, be sure to roll down your car's windows halfway to equalize the pressure of the shock wave. Otherwise your car could end up with crushed roofs and shattered glass like many in the accompanying photos. Read the whole document here for tips on how to survive nuclear war and the aftermath in your car. While it's true you might fair pretty well in your car, there's little mention of the ensuing radioactive fallout except that you should roll your windows up as soon as possible to protect yourself from the dust. Yeah, right.
Looking through the photos from the National Nuclear Security Administration, it would seem someone either had it in for the Ford Mainline or got a great deal on a whole bunch of 'em. There's also a photo of the tragic sacrifice of a woody wagon that held up much worse than that Cadillac.