Well, if you don't mind using a 3-word pop-culture reference for this, you can use "Kobayashi Maru scenario".
In the scenario of the 2280s, the cadet receives a distress signal stating that the civilian freighter Kobayashi Maru has struck a gravitic mine in the Klingon Neutral Zone and is rapidly losing power, hull integrity and life support. Sensor readings are indeterminate and there is no way to verify the distress signal. There are no other vessels nearby. The cadet must quickly take a decision:
Attempt to rescue the Kobayashi Maru's crew and passengers, which involves violating the Neutral Zone and potentially provoking the Klingons into hostile action or an all-out war; or
Abandon the Kobayashi Maru, potentially preventing war but leaving the crew and passengers to die.
The objective of the test is not for the cadet to outfight or outplan the opponent but rather to force the cadet into a no-win situation and observe how he/she reacts.
And it would perfectly fit the OP's original statement:
The American government has decided to pour extra money into the war in Iraq, unable to escape the Kobayashi Maru scenario it has entered.
(P.S. And, yes, we all know that Capt. Kirk was able to beat the Kobayashi Maru scenario, but he finally had to admit he cheated to do it.)