This may depend on the type of Debt Consolidation Program you want to use. It is likely that any Debt Consolidation Program you will choose can save you a large amount of money when compared to the very minimum payments. You may use a debt calculator to look at your specific situation and how much you can save.
If you are still making the minimum monthly payments on your credit card debt, the chances are high that you're mostly paying just the interest, and not paying down the actual principal amount by much if at all. This won't make much of a dent in your ovarall debt. And if you miss your payments or exceed your limit, your credit card interest rate will only go up. Replace your credit card debt with consolidation loan, where your interest rate won't change and your principal loan amount gets paid down as you make fixed monthly payments.