The Constitution gives Congress the power to declare war, and the President discretion for the details of how to fight the war.
Congress doesn't authorize each troop movement and each battle. That would be silly. The President has some discretion. However, Congress does have the power to declare war.
With the War Powers Act, Congress partially delegated its war-declaring power to the President. For 60 days, the President can deploy troops without Congress' authority, but only if it's an emergency. This law may be Unconstitutional, but Congress and the Supreme Court haven't rejected it.
The "war in Libya" has lasted more than 60 days. That puts President Obama in violation of the War Powers Act. Plus, Libya's problems were never an emergency for the USA, making the initial deployment a violation of the War Powers Act.
Unfortunately, the President will almost definitely get away with it. If Congress feels offended, their only recourse is impeachment. There's no way Democrats would vote for that.
Congress should just do away with the farce. They should say "The President can do whatever he wants." That would be more honest that a complex system pretending to follow "rule of law".
The President and the police can do whatever they want, with practically no restriction.
- The President can declare anyone a terrorist and murder them without a trial, whether they're a US citizen or not, no matter where they are located.
- The police can search your property without a warrant or reason. You aren't allowed to resist.
- Via "asset forfeiture", the President or police may seize your property, without trial.
- If accused of a crime, you may be held indefinitely without bail.
- Via income taxes and other taxes, all your labor and property belongs to the President and the State.
There is no rule of law in the USA. The President and insiders may do whatever they want. If you're targeted by a State prosecutor, he'll say "The law must be strictly enforced as written!" When insiders commit crimes, there always are excuses and loopholes.