How much do I have to save for a debt management plan?

As far as I know, there is no definite amount you need to save. Talk to a good organization to enroll in a DMP.

It depends on the following factors:

1. The debt management fee that you have to pay to the credit counseling agency
2. The total amount you owe on your credit cards
3. Your monthly payment amount the completion of the negotiation process

It's better to start saving at least 10% of your monthly income every month.

There's no minimum or maximum amount of saving required for a DMP. But you may need to calculate how much your monthly payments are gonna be. Based on that you should save money from your paycheck. AS SC said above, you can start saving at 10% initially from your paycheck, and increase the amount later.

You don't have to save as such to enroll in a DMP. However, you need to pay a significant amount to the debt relief organization (who's offering the DMP) to repay your debts systematically within a definite time.
A DMP company is not supposed to charge anything upfront. So, beware of a company that charges to enroll. Moreover, you should choose a reliable company to manage your debts and pay them off.

Debt management plans reduce interest rates, but your payments remain around what they would be when paying minimum payments. The point of this program is to get out of debt faster. If you need more a reduction in your payment then you may want to use a hardship program like debt settlement.