Since Truman, presidents, both Democrat and Republican have been engaging the US in unconstitutional wars. The Constitution is very clear about declaration of war; only Congress can do so. But I have trouble calling that,"illegal". Vietnam, Grenada, Panama, Iraq I, Kosovo, Iraq II were all unconstitutional, but each time, Congress was consulted. Not so for Libya.
The War Powers Act allows the President to commit combat troops for 60 days without consulting Congress in the event of "imminent hostilities" against the US. No such conditions exist. The argument can be made that the case existed for each of the previous wars listed, but the President has made clear that it does not exist for Libya.
Grounds for impeachment.