As a public service, we at the Posse are pleased to offer a little free advice to help resolve the budget impasse.
For starters, don't insult your negotiating partners. It may score you points with your own extremists, but all it does is make an agreement that much harder to achieve.
Next, focus on points of agreement rather than disagreement. Look for areas of common ground, not places where you can pick each other apart.
Finally, in dealing with a fractious organization, try to isolate the moderates from the extremists by offering modest concessions. These will give the moderates cover and force the radicals into an untenable position.
What you should not do is draw such a hard line that moderates believe that agreeing with you is political suicide. That is what the extremists want them to think. You are only playing into their hands.
Of course if your true objective is the total destruction of your enemies, at least be open about it - and don't be surprised if they turn to the biggest firebrands they have to fight you off.