That's a tough situation. It doesn't sound like you are willing to quit and it sounds like the contracting agency knows that or doesn't care if you do. That leaves you personally with little leverage.

The person who does have leverage is person who makes hiring decisions. But this isn't a definite either. Being that it's the govt I imagine they have approved vendor lists and can only use those contracting agencies. If your agency isn't the only one on that list and your boss is willing to go to bat for you then you have leverage. The agency cares more about their relationship with your boss then they do about you.

If your boss won't exert pressure then I think your only recourse is to accept the money and look for a new job while keeping your current one.

-Dylan