There's no way in the world he's going to be impeached because of this, because the decision to bomb Libya was a decision of the UN, and was supported by them as well.
loving republicans, conservatists, bashing the president every second they can...
Obama didn't need the permission of Congress, because it wasn't even his idea. It was the suggestion of the UN, and he needed to work fast.
BTW, Obama doesn't personally launch missiles from the Oval Office, he gives instruction to the military to do so, meaning if he didn't have congress approval and decided to bomb on his own, there's no way it could have happened because I'm certain the people in charge of launching the bombs would have confirmed with congress that it was approved. Then we would have just heard that he tried to launch the bombs.
BUT THAT'S NOT THE CASE.