Usually negotiating creditors will agree to take less on a lump sum amount. There are a few drawbacks to making one payment to eliminate a debt, but generally they're short lived. Sometimes the creditor will come to you, sometimes you have to go to the creditor.
If you're current on payments, the creditor is less likely to accept a lump sum. They're of the opinion that since you're paying on your debt, you're still good to pay them everything, including interest. Calling them up and saying that you'd like to settle the debt for an amount of money that's less than the current balance will most likely not be taken seriously.
It's suggested to stop making payments for at least a couple of months, then approach the creditor. This results in a hit to the credit rating as late payments will get reported. The flip side is that the creditor will now be more likely to negotiate for so many cents on the dollar to get rid of troublesome debt. A complete payoff of the balance will result in an improvement of the overall score as there is less debt being shown. How much impact on the credit report depends on individual circumstance.
A debtor looking to settle their debts is best served by talking with a lawyer that specializes in debt settlements. They'll be able to give advice on what to expect from a settlement. A benefit of hiring one is that they work to negotiate the best possible deal for their client.