First of all, I'm sorry to hear about your situation. Being behind on credit card bills, on top of being unemployed, has got to be incredibly stressful for you. At a minimum, you should resist the temptation to make any further charges and dig yourself any deeper in debt.
But to answer your question, if you stop paying your credit cards, as you can guess, you'll start getting calls from debt collectors, and eventually you'll probably start getting stern letters from attorneys.
I'm not a lawyer myself, but I can tell you that what will almost certainly happen if you stop paying your credit card bills altogether, and ignore all the phone calls and letters, is that eventually, either your credit card company, or whoever they've sold the debt to, will try to take you to court. Then things can get serious. Debtor's prisons are a thing of the past, but you could see your wages garnished after you do find a job, plus you'll have the burden of paying court costs, and so this debt and all of its headaches could be with you for a long, long while. And, of course, your credit score, not to mention your savings, will be heavily depleted when it's all over.
But don't despair. I'd recommend you find a local debt counselor through a reputable credit counseling service like the National Foundation for Credit Counseling (website: www.nfcc.org). They'll either be able to negotiate with your credit card companies, so you can make smaller payments, or they'll steer you to a good bankruptcy lawyer. I know bankruptcy isn't what anyone wants to hear, but if your financial life is already in tatters, I'd vote for bankruptcy rather than lawsuits any day. A fresh start will help you rebuild your credit score and history once you get some income flowing, which is only a matter of time.