The Obama administration has tried to justify continuing the war in Libya without congressional approval by arguing that its military actions do not constitute full-blown hostilities. I've tried this line of reasoning with my mother when I was growing up. I used to say, "I only beat up my brother a little bit. It didn't constitute full-blown hostilities, so I shouldn't get in trouble." It never worked. Ma knew not to buy that line of bullshit.
The fact remains, war is war. Seems simple enough. All the legalese in the world can't change it. Either President Obama needs to seek congressional approval to maintain the war in Libya or the war needs to stop.