Consumerists, How Do I Deal With Credit Card Companies Now That I've Lost My Job?

Newly unemployed, credit card debt-carrying Lilgaladriel wants some advice on how to deal with the credit card companies. He writes:

So I’ve recently become unemployed, and I have 2 credit cards that I’m paying off — one with Chase and one with Discover. I’m already on special payment plans with both of them in which the APRs have been decreased to about 12% and and further purchases are blocked. (FYI, my balances are roughly $6,000 with one card, and $4,000 with the other.) I’m wondering what would happen if I called the companies and told them that I’m now unemployed? There’s no way I’m going to be able to make any more payments until I find a new job; I have absolutely no savings at the moment — saving hasn’t been at all possible for me to do. What do most people do in this situation? Are the CC companies going to tell me to suck it up?

Advice — solicited or otherwise — is what Consumerists do best, so have at it. What are Lilgaladriel’s wisest moves to avoid drowning in payments?