It is an interesting argument, but it seems to be completely absurd. It is illegal for a Libyan soldier to fire at coalition forces that are trying to kill him? How does that not violate another principle of international law - the right of a sovereign to defend itself? Yes, there is a Security Council resolution granting its forces the right to set up a no-fly zone and take other measures to protect Libyan citizens; however, a reading of the resolution does not explicitly prohibit Libyan forces from fighting back. That might be an implied condition of the resolution, I'm not sure because my knowledge of that particular area of the law is lacking. Even so, I don't see how UNSCR 1973 can strip the right of a country's armed forces to protect its homeland and make it illegal for them to fight back.
While I agree with Tushnet's ultimate point - that the Libyan intervention is not a war - I've got to disagree with his argument and go with my original argument that it isn't a war because the scale and nature of U.S. involvement is not yet sufficient to make it one.
Bobby Chesney has a more informative post about this at Lawfare.