I haven't tried the program you mentioned, but just from looking at info about it, I would not spend money on it. It looks like advice that you can get free other places. If you pay extra on your debt, of course you will pay it off faster and pay less in interest. Take that money you would pay for the program and make an extra payment on your credit card instead.
I like the method Crown Financial advises on paying off debts faster. You can read about it here: http://www.crown.org/LIBRARY/ViewArticle.aspx?ArticleId=765.
And here's a calculator you can use to see how it would work for your situation: http://www.crown.org/Tools/Calculators/Debt_AcceleratedPa...
Basically, the method is to first stop adding to your debt. Second, make a list of all of your debts--the amounts, interest rates, and minimum payments--and put the list in order from highest interest rate to lowest.
Then each month, pay the minimum payments on all the debts, except the first on the list--the one with the highest interest. Any extra money you can pay each month should be applied to that first debt on the list. ANY extra money you can pay means less interest you will owe and the quicker you will pay it off, so pay as much extra as you possibly can.
When the first debt on the list is paid off, don't consider that amount you were used to paying (say it's $100 a month) as free money now. Instead, "roll it over" to the amount you will pay to the second debt on the list. So now you are paying extra on the second debt every month. When the second debt is paid off, take that same amount and apply it every month as an extra payment to the third debt. Each time a debt is paid off, the whole amount gets rolled over to the next debt, so pay off is accellerated.
Another thing to keep in mind, as your debts are paid down and the minimum payment required is less, don't lessen the payment you send. For example, if you used to send in a required payment of $50, and the minimum payment is lowered to $40, keep sending the $50. That extra will help pay the debt quicker.
Good luck with it all. And Happy New Year!
PS--I looked up Dave Ramsey and his method is similar to this one. He calls it the "snowball" instead of "rollover", but it's the same idea. Only, he has you list the debts in order of smallest amount owed to largest. If you do that, you'll see the first debt paid off more quickly and be encouraged to continue. But the advantage to paying off the highest interest debt first is that you will save money by throwing away less in interest.
You could always compromise by alternating low balance and high interest debts on your list. But the main idea is to pay as much extra as you can, and when each debt is retired to move that amount you've been used to paying and apply it as additional payment on the next debt. It takes self discipline, but you can do it!