The grocery chain that owns all the stores in your area was expanding rapidly in the last couple years, and went into large amounts of secured debt (i.e. mortgages) to do it. They used this money to build new stores, warehouses, shipping depots, etc. They even have a line of credit for covering cash flow needs for purchasing inventory before they can sell it.
Now, we have the current situation. Their real estate values have to be marked down, even though they have no intention of ever selling the properties at a profit. They are now in a negative equity situation on paper. This violates the debt covenants on their rotating line of credit. They can no longer purchase anything until they have hard cash.
Stores in most areas do not have much of a cushion in terms of their inventory supply--usually nor more than a week, and often less for perishables. While the run off in some of their inventory happens to build up enough cash to make purchases, people see the shelves emptying and panic. People hoard whatever they can, leaving lots of others with no food reserves.
Now, you might say, this solves the problem. They should have enough liquid money now, especially if they stop making some of their debt payments temporarily. But you've got some period of time where people are out of luck.
Now, what if this happens to some segment of their middlemen or end chain suppliers instead? What if the lenders for these lines of credit go bankrupt themselves? What if people simply start pulling lines of credit because of fear?
This possible chain of events are what people are talking about in the "Seizing up of the credit markets". In this country (and in large portions of the rest of the world), we have built up a system where almost everyone borrows for almost everything...from end customers all the way up the value chain. When this system breaks, the results are so unpredictable that no one really has any clue of what would happen--so the potential for a worst case scenerio needs to be the one which is considered.
Now, people probably wouldn't starve. They'd just have to live on rice or some other staples for a few months. Most people would probably not loose their jobs--but a large portion would, and this feeds back into the earlier problems. You have entered a positive feedback loop, and it's impossible to predict just how bad things could get.