Debt Consolidation

Recently I contacted an agency regarding debt consolidation. They set up a payment plan and sent autorization papers for the first payment to be automatically withdrawn from my checking account. In reading the contract, I noticed that it stipulated that the entire first payment was to be a "deposit" paid to the agency (and refundable upon completion of the contract.) However, this means that my creditors won't receive payment for one more month. The agency informed me that credit card companies require this "deposit", and once it's made, will stop calling. Does this sound right?

Also, will it hurt my credit more to enter into consolidation or to let the already past due payments go for another month or two before I can start catching up on my own.