We have a long history of waging undeclared wars. There is natural tension between the president's powers of commander in chief to initiate military action and Congress' power to declare war. In between, you have Congressional power of the purse to restrain a president.
John Yoo, who does have that law degree and plenty of experience, does not think much of the argument that the war is unconstitutional, and writes:
As I’ve explained in an earlier post on The Corner, and in more detail over at Ricochet, I think this view of war powers is mistaken as a matter of constitutional practice and of the original understanding of the Constitution at the time of its ratification. I won’t repeat those arguments here, other than to point out that the Constitution gives Congress a singular, unique tool to stop any war it disagrees with — the power to cut off funds. If these senators think that President Obama is waging an unconstitutional war in Libya — and I would be the first to admit that the conflict does not involve an actual or imminent threat to the nation’s security — they should refuse to approve any appropriations for the Defense Department that would go to pay for our military and intelligence operations there. I hope that these Republicans will reconsider their views after giving some deeper thought to the way that the separation of powers really works.
Congressional opponents of the war can't rely on the constitution to nullify the war and spare them the responsibility of using their powers--if they dare--to end the war. I think the war is clearly constitutional (as would be efforts to defund it, of course), and would rather win it than starve it of funds. We'll have to change how we fight to win, but as long as we are fighting there is hope we'll get it right. Or get lucky. I can't rule out the possibility of a magic shell fragment dropping Khaddafi.