Contingent state of war?

The law of nations actually defines what is "war" with enough precision to cover the present events in Libya. An act of war makes it war. Bombing a country is an act of war, unless it is some kind of training exercise, at the invitation of the government of the country. It is apparent that is not the present case. On the other hand, there is some confusion as to what is the government of Libya, or whether it even has one. Qaddafi asserts no title of office, so by the standards of the law of nations, he is a kind of pirate, not a head of state. No declaration of war is needed to attack pirates, just as we did not need one to attack the Barbary Pirates. However, the attack needs to be, to the extent possible, focused on the pirate personally, not on military assets of the country, no matter whom they are taking orders from. Therefore, it is constitutional to take out the command center from which Qaddafi is operating, even if it kills him, without a congressional declaration of war or letters of marque and reprisal, provided the collateral damage to anyone not associated with Qaddafi is minimal and compensated. There may be a reluctance to make a martyr of Qaddafi, but taking just him out is the appropriate course of action in this situation, if it can be done. However, the attacks already made exceed the bounds of just taking out a pirate and his henchmen, so a state of war exists unless an internationally recognized government of the country consents to the attacks. That is likely if the opponents of Qaddafi prevail, but is not if they don't.

The Constitution did not really contemplate contingent states of war, in which one side consents and the outcome can decide whether there had ever been a state of war.

All the President needs to do to legitimize his action is to recognize the Benghazi regime as the legitimate government of Libya, as France has done, and get them to issue an invitation to conduct exercises on its territory. It's not "war" if it's by invitation of the host government.