First, I believe that the president's power as commander-in-chief of the military is very simple to understand. He has the power to give any (lawful) order to anyone in the military, and it must be obeyed. That includes things like ordering the military to blockade, bomb, or even invade Afghanistan, Iraq, Libya, Syria, and Iran.
However, the definition of a lawful order is limited by both international law -- which means treaties that the U.S. has signed, and more importantly the "law of war" that says things like you're not allowed to harm, and in fact have a duty to protect, civilians, prisoners, and anyone else who doesn't try to harm you or disobey your orders.
Furthermore, lawful orders are restricted by the specific rules that the U.S. military follows, such as the Uniform Code of Military Justice, and that's set by Congress, as specified in the U.S. Constitution, Article I, Section 8, Paragraphs 10-16 and especially Paragraph 14, "To make Rules for the Government and Regulation of the land and naval Forces."
That means if Congress wants to specify that "No member of the armed forces of the United States shall enter Libya," they can do it. And they can certainly specify the various conditions listed in the War Powers Resolution.
That being said, I am all in favor of intervening in Libya as long as we do it good and hard. In fact, I'm in favor of intervening in Syria even better and harder, since Assad is worse than Qadaffi. And if Iranian Revolutionary Guard units are in Syria, that gives us a really good excuse to attack those units.
On the other hand, I will also repeat what I warned about before we went into Afghanistan and Iraq, which is that we need to have a clear plan, including a clear objective. Glenn Reynolds is right: "Waging war halfheartedly, on the cheap, and by committee is not a formula for success."