If your only concern is federal student loans I wouldn't worry about it. Your credit will take a ding and that's what you should be concerned about. Ask for a PTD (pay to delete) and if they agree then get a written letter sent to you with the terms, sign it and return it with the amount agreed upon. Usually PTDs are more expensive than the principal. So you can chalk up paying $3k+ now or possibly paying more than that in interest rates over the course of the next few years if you take out any type of loan. Generally, with a score in the 750's you'll see a more significant drop in your score than a person with a score of, let's say 600. Basically, the higher your score the more it will drop.
I would look at the language in the actual contract and see if there is any way you can expose a flaw in their language. If it's just a 1 page agreement you'll likely lose on this front, but if it's multi-page contract with inclusive language you might have some wiggle room. Lawyers and linguists are helpful here. It's amazing how much you can make implicit language work in your favor if you know how to spot it--cell phone and utility contracts are notoriously bad about this, which prompt constant amendments to their contracts.
$3k is petty is the scheme of things with a 750 credit score though. Work out a payment plan, just pay it, or PTD--your future interest rates with thank you.