Just keep making the payments and send them a certified letter that you're willing to continue making the regular payments but there is no way you can pay the lump sum. If they start refusing to take your payments, that suggests more trouble is brewing and complicates the solution. I have seen many lenders look past the default if payments continue to roll in.
Agree with Ronald, in the short term, all you can do is keep making the payments. I would send a certified letter requesting reinstatement of the loan. If push comes to shove, you may end up litigating the validity of that clause in the contract.
If the amount of student loans are high, settlement may not be such a bad thing if you can pull together the resources to do it. One area of my practice is settling private student loans for clients. It can be a good option and does not always require a single, lump sum payment.
Keep making your payments. If the student loan company and or collector will not negotiate, google IBR Student Loan, (look for the .ed.gov to ensure you are in the right place). It is a government program called the Income Based Repayment program. If your loans are federal, you may qualify and take the collectors out of the equation.
This answer is general and is not intended to create an attorney client relationhsip and is for informational purposes only.