They have not been able to declare war on the entire world, including their own citizens, before now. Assassination has not been an accepted tool of foreign policy for decades since Ford.
Even in wartime (if this is indeed war), rules apply, so if you want to apply the rules of war assassinations of enemies who are unarmed and not on any battlefield are not permitted. Awlaki, and later his teenage son, and the innocents killed with them, were not killed on any battlefield or as part of any war, unless you redefine war to mean any killing outside the judicial process, as Bush and then Obama have done.
But I think it's more useful to consider the methods used rather than arguing about semantics - the US president now claims the right to kill citizens, and anyone else, without trial or justification. That is a huge shift in policy and also has implications at home. If they can kill at will abroad, why not at home?
The whole concept of rules to warfare is on a certain level a bit silly. As if the hawks can add rules to warfare, they can make it more palatable to general public and then wage war more frequently. On other side of the coin, if war is just so horrible (many innocents and civilians needlessly killed), then warfare as a business practice for the state will become less frequent. To a certain extent, the threat of global thermonuclear war has somewhat borne out this line of reasoning.
The constitution requires a declaration of war. That requirement has been withered away in recent years, don't you think? It was there to prevent exactly this sort of nonsense.
Article I, Section 8 says that Congress has the power to declare war. It does not specify that this declaration need take any particular form. I've never seen a convincing explanation for why Congressional authorization such as the AUMF doesn't qualify as an exercise of Congress's powers under Article I, Section 8. Especially considering that the practice of Congress authorizing military actions without a formal declaration of war dates back almost to the founding: http://en.wikipedia.org/wiki/Declaration_of_war_by_the_Unite....
To be fair, a large part of why America doesn't declare war is because no-one declares war. After WWII we no longer consider war-making a sovereign right of nations, so a declaration of war is useless.
First, no, it doesn't. It gives Congress the power to declare war. It neither explicitly requires nor has ever been understood to implicitly require a war be declared to be prosecuted in all circumstance, particularly not in the event of a war initiated by an enemy attack.
Second, as with every other Congressional power, exercising the power to declare war doesn't require any kind of magic words. All of the controversial drone attacks on al-Qaeda targets have been as part of action specifically authorized by Congress in Public Law 107-40 [1].
Whatever problems there are with the War on Terrorism, the absence of Congressional declaration of war certainly isn't one of them.