Game Theory gives us a simple lesson about negotiating with Terrorists: DON'T DO IT. Even if the Terrorist is demanding $2.50 and a coke in exchange for not annihilating Europe, you CANNOT give them anything.
The incentive to negotiate is simple; you can forestall deaths or destruction for some smaller sacrifice. So why not negotiate, under any circumstances? Because of the next threat. If someone has to kill some hostages to get some concessions in negotiations, then those concessions have killed untold number of future hostages. You can save some people in the room, but you've encouraged future attacks for the rest of time.
This is why Obama's reasoning on the tax cuts is wrong. He directly invoked the hostage argument, then did the exact wrong thing. Obama said that you don't negotiate with hostage takers, unless the hostage may get hurt. This says that any time the Republicans want anything at all, they only need to tie the bill to some looming disaster. Instead of putting the hostages at risk this time, Obama has put two years of future bills under the same terrorist threat.
EDIT: Let me make this clear: by appeasing the Republicans, Obama has ensured that Republicans will sabotage every necessary bill until the last moment. Once a bill's passage becomes an emergency measure, the Republicans will present a series of new demands. Obama will presumably surrender to whatever the Republicans want at that time. The Republicans will still pass the bill, so they will receive no political backlash.