First off, must make a few assumptions-Since you have gone with the credit counseling service, then you must be satisfied with your credit card debt situation. So I will not address that other than the decision of whether to discontinue that and go alone.
I agree with Charlie above that dealing with the CC companies yourself will probably save you money. The counseling service is just another layer between you and your spending problem-which hopefully is over now that you have gotten this far.
My second suggestion would be, make sure you are planning your spending, and maximizing your income. The two ways to get out of debt are to make more money, and spend less so that you can make progress on your loans. The hard part is sticking with the plan. But every time you are tempted to overspend, remember how much you hate those collection calls.
My third and last suggestion is participating in a group such as this or something similar closer to home, that will allow interaction, opportunities for learning, and most importantly support in your efforts to get to freedom in your personal finances. This is a process.
Now to your question of more or less in emergency savings. My rule of thumb is that if you can get out of debt with all the above going at full bore in less than 18 months, then a small emergency fund such as yours is ok.
If you anticipate you will take longer than that then a larger fund would be in order. How much would depend on a lot of factors such as job loss risk, your family situation,(3 kids in diapers would be different than a single guy), and your risk tolerance.
Congratulations on making the decision to deal with it and good luck.