Stay in School until the Job Market Improves?
For decades it's been a common strategy that's worked out pretty well: If the job market is crappy when you graduate, find a way to stay in school for a year or two—add a second major, go to grad school, find a post-doc. This time, that's not looking like such a good idea. (See also: A Society of Fear)
It used to be, even though an extra year or two of school meant a year or two when you were hardly earning any money, you'd still come out ahead—because the higher starting salary you got entering the job market at a more favorable time would be the base for all your future raises.
That worked great in the days when being a student merely meant that you were broke. Now, being a student means you're going into debt to the tune of tens of thousand dollars a year. If that's what you're doing, you're probably digging yourself a hole that you'll never be able to earn your way out of.
Only time will tell what the new winning strategy will be, but my best guess is that you'll still want to avoid beginning your career during a severe downturn. You'll just want to do it without adding to your debt load.
If you can mark time without growing your debt—for example, as a grad student with an adequate fellowship or assistantship—then go ahead.
If you can't stay in school without taking on even more debt, consider making a temporary entry into the job market. Don't begin your career, but find some paid work that lets you support yourself. Then, when the market looks like it's finally turning around, do something to mark a break with your temporary work and then begin your career.
The obvious thing to mark that break would be to go back to school for the second major or the advanced degree, but that's hardly the only choice. Others would be to take on an internship, do an open-source project, volunteer at a non-profit, start a small company, or write a book.
The point of the break is simply to make it clear that what you were doing before wasn't a failed career, but was rather (like a string of post-docs) just something that you were doing before beginning your career. (My article Fund Your Own Sabbatical is on-topic here. The issues, in terms of taking a break and then reentering the job market, are largely the same.)
The way we fund undergraduate eduction in this country is already leading to a whole cohort of new workers who will be permanently indebted. With a bad job market tempting them to stay in school, the unavoidable additional debt load is just going to make things worse. It's reasonable to be leery about entering the job market during a downturn, but taking on even more debt is not a better choice.