There have been numerous media accounts of plant shutdowns (largely in the auto industry) as the result of a cutoff of the supply of parts from Japanese manufacturers due to the earthquake/tsunami/nuclear disaster. These accounts are somewhat misleading.
While these disruptions may lead to reduced supply of some types of products, they will almost certainly not lead to overall shortages in the market. In other words, there may be some cars that temporarily will be in short supply, but it is almost inconceivable that there will be a shortage of cars more generally. This means that car buyers may switch brands; they will not be unable to buy a car.
In this case, the shutdowns of certain factories are likely to be offset by increased production at other facilities, with the net effect on the industry being close to zero. The shutdowns are of course bad news to the workers affected, but they will be of little consequence to the economy as a whole.