He doesn't have that authorization. The attacks are continuing.
To begin with, this law was broken when the attack was initiated. The President may only introduce the use of military force when
- there is an declaration of war
- specific Congressional authorization
- a national emergency in which the United States is being directly attacked.
To make matters worse, even if the attack began legitimately, the War Powers Resolution does require Congressional authorization within 90 days. We have passed that mark and the President continues his attack with Congressional authorization. Pretty clearly, this law is being broken by the executive branch.
The written excuse put out by the President is beyond contemptible. Basically, the argument is that this is a small conflict, so it doesn't count. Go back to the War Powers Resolution and you'll note that there is no exception made for small conflicts, or those involving low probability of casualties, or not having boots on the ground. If the President wishes to use military force against another nation, he must have Congressional approval. No exceptions are made in the law.
The War Powers Resolution fills a necessary hole in our division of power, as military action may be necessary before the slow gears of legislation can catch up to a national emergency in our modern age. Pretty clearly, Libya was no threat to our nation; if we wished to change their regime or stabilize the region, those are reasonable objects, but they require a national discussion followed by approval from the branch closest to the People. The President's action is nothing more than a naked power grab, which unfortunately will pay off for him. There is no real judicial recourse to end the campaign; no court writ will undo Libyan lives ended by American missiles.
I've pointed out elsewhere that the political and moral reasons for this Libyan intervention are pretty ridiculous as they could just as easily apply to Syria, which the Administration has shied away from. It looked like an easy opportunity to have a rally 'round the flag effect and show the United States supporting purported democracy lovers in the Middle East. Clearly, that has not been the case. That the President is so willing to break the rule of law is most distressing. Some modification to the War Powers Resolution is required in order to give it judicial teeth; if a law cannot be enforced, it is not a law.