I was having trouble following. Probably my own denseness.
If we put aside the Constitution (as it seems happens far too often) then any whim would be a valid reason for a war.
I admit that the constitution is not as clear as I would hope, which is why I was honest in saying I didn't know how "hard and fast" the constitutional rule was.
The enumerated list gives congress the power to declare war. They cannot wage war. Congress can also call for the army to be put into play but do not get to direct its actions: "To provide for calling forth the Militia to execute the Laws of the Union, suppress Insurrections and repel Invasions;" The reasons given for congress to call the militia would be to suppress insurrections and repel invasions. I have no doubt at all the founding fathers did not intend for he insurrections being suppressed to be in other countries.
The President on the other hand can wage war but cannot declare it. Once the services of the army are called be directs their actions: "The President shall be Commander in Chief of the Army and Navy of the United States, and of the Militia of the several States, when called into the actual Service of the United States" He can only direct their actions in the service of the US.
Putting those two limitations together we see that a war must be waged in the service of the US and declared to suppress insurrections or repel invasions (or execute the laws of the US).
The humanitarian mission in Libya meets none of those except when one stretches the law beyond reason. The fact is that the constitution does not even allow the expenditure of money for humanitarian causes here in the US much less abroad, and since wars cost money...