From the article:
"The administration followed an unusual process in developing its position. Traditionally, the Office of Legal Counsel solicits views from different agencies and then decides what the best interpretation of the law is. The attorney general or the president can overrule its views, but rarely do.
In this case, however, Ms. Krass was asked to submit the Office of Legal Counsel’s thoughts in a less formal way to the White House, along with the views of lawyers at other agencies. After several meetings and phone calls, the rival legal analyses were submitted to Mr. Obama, who is a constitutional lawyer, and he made the decision."
Sounds like Obama had a feeling that the DOJ would not support his legal analysis and so devised a less formal process whereby he could circumvent their legal conclusions. It is telling to me that attorneys from the Pentagon supported the DOJ view, as they would be the agency most affected by the decision to get involved in Libya.
I find this issue interesting not because I think it will really affect Obama in his reelection bid or that he could face impeachment (both unlikely), but because I think it signals a new era in how our government approaches military operations. If the Obama analysis that no American personnel getting shot at = no "hostilities" stands then I would expect much less Congressional input into future military endeavors as our armed forces move to more unmanned missions.
To me, the test of whether we are engaged in "hostilities" is very simple. I would ask, "If another country did this to us, would I consider us at war?" Evidently, the President disagrees.