when to call credit card companies

Hi,
I've been struggling for the past few years with debt (7 different credit cards) and have been able to pay at least the minimum due each month. But now it's gotten to a point where I won't be much longer anymore (loss of job, savings depleted...). But instead of declaring bankruptcy at this moment, I'd still like to pay them back somehow so it won't kill my credit report. And rather than having the ridiculous interest rates pile on and the additional late fees which makes things so much worse, I've heard that sometimes those credit card companies would be willing to reduce the interest rate, late fees, discount payments... So my question is this, how many months should I wait after I stop paying the monthly minimum before they get worried enough so would be willing to negotiate with me? I've already tried talking to them when I was still paying them on time but they told me they wouldn't be able to work with me because my account was still in good standing. So I guess I can only get them to lower the rates or whatever is by completely stopping paying them altogether? Any experience/thoughts/suggestion is greatly appreciated.

Jeff