In 1997, under intense lobbying from student loan companies, the Higher Education Act was amended, and defaulted student loans became among the most lucrative and easiest to collect type of debt. These amendments allow for huge penalties and fees to be attached to defaulted student loan debt, take away bankruptcy protection for student borrowers, dissallow refinancing of the debt, and also provide for collection and punitive measures to be taken against student borrowers, including wage garnishment, tax garnishment, withholding of professional certifications, termination from employment, social security garnishment, and others.
The author of Sallie Mae Is Ruining My Life (a blog that has since vanished, and I can't find an archive) wrote that he started out with a loan of $38,000 at 5% interest, and in one year, through practices made legal by political bribery, Sallie Mae turned it into a debt of $70,000 at 18% interest, and harrassed his workplace until he was fired. Private lenders do not want you to pay off the debt -- they want to increase the amount you owe, forever.
On the surface, the Department of Education appears to only take over "Direct Loans", which means money you borrowed directly from the DOE, and not via a bank. But on the Direct Consolidation Loans page, in the eligibility section of the FAQ, is the secret password info for people who have all of their loans from Joe-Bob's Bank of Suckiness, Sallie Mae, or some other non-government entity:
Borrowers who do not have Direct Loans may be eligible for a Direct Consolidation Loan if they include at least one FFEL Loan ... or have been unable to obtain a Federal Consolidation Loan with income-sensitive repayment terms acceptable to them.
So what you have to do is call the DOE (1-800-557-7392) and say "I can't get a Consolidation Loan with income-sensitive repayment terms from my current lender! Help! I'm broke! I want to pay, but they won't give me a chance!" etc.
If the first person you reach seemes confused, try again the next day with a different representative. No matter what info you get (positive or negative) call until you get a second person to confirm it. (Just say you forgot what they told you, or whatever.) This is the government, remember, incompetence is their hallmark! They don't hate you, they just don't really care. You are trading intentionally evil and predatory owners, for largely distracted and vaguely incompetent ones! This is a good trade.
If I recall correctly, and it has not changed, the DOE sends a form (either to you, and then you send it to your lender, or they send it straight to the lenders themselves) on which the lender basically agrees that "No, we can't offer this person a payment level they can meet." Or words to that effect. The way to get your private lender to dump you (assuming you are fairly poor) is to demand an Income Contingent Repayment (ICR) Plan, which you can find in the Glossary section of the page above:
A repayment plan that bases your monthly payment on your yearly income, family size, and loan amount. As your income rises or falls, so do your payments. After 25 years, any remaining balance on the loan will be forgiven, but you may have to pay taxes on the amount forgiven.
Once you get this, you can still pay more whenever you want, which will knock your principal balance down faster. But you will not be forced to make too high of a payment, nor will being unable to make payments force you into evil things like interest capitalization, which explodes your debt.
You are promised the "income contingent" option under the law, but most people know nothing about it, and your lender will never tell you! Just keep calling them and demanding this by name, and refer them to the US Dept of Education website and keep saying "Legally, you have to do this, and if you can't or won't, then you have to sign the paper to let me consolidate directly through the government!"
Do not consolidate with a private entity if you can avoid it, and especially not with Sallie Mae. They will say anything to keep you and increase your debt. They will offer you cake and sex and fairies and the moon -- and then they will ride you like a rented mule until you die.