Get out of federal student loan in default through a lump sum payment or a rehab program?

I recently got a call from a collecting agency on behalf of the Department of Education about a federal student loan I took out a couple years ago, which went into default. The agent offered me two options. Either I pay everything back in full, or I enroll in a rehab program to get out of the default first and then work my way up. Even though it is a pretty big sum and it will take me some work to get that amount, it is not entirely beyond reach. Now my question is, which route should I take to go about this? DOE already put some negative items on my credit report. I am guessing if I pay them the lump sum, they would change the status to "paid in full"? And how would that impact my credit rating? If I go with a rehab program instead, how would that look on my credit rating? I am just worried that the interest would climb to an insurmountable sum while I am still in rehab. And they are basically waiving off the collection fee if I pay in full. I know that any amount written off is taxable through 1099 but I am not sure what % it typically is. Not really experienced in the subject so I can really appreciate some inputs. Thank you!