Al Jazeera English is reporting that Gadaffi has rounded up some of the western journalists in Tripoli (they were already nicely contained in a hotel somewhere) and bussed them off to the fortified compound where he is holed up.
Where they would be killed by any decapitation air strike against him.
Any thoughts of a decapitation strike against Gadaffi and his sons will have to take into account his wiliness. He survived such an attack by the U.S. once before. In Reagan's 1986 U.S. air strike against Libya (in response to the Berlin discotheque bombing) Gadaffi was targeted, but he and his family escaped by fleeing their residence at the last minute (reportedly warned by the Italians when U.S. aircraft overflew Malta's airspace en route to their targets).
So he fears such an attack, but he's been preparing for it a long time. He'll make it impossible to get to him without unacceptable collateral damage.
All of which goes to show that military response can only go so far to resolve the problem. The end game would have to be a deal for Gadaffi to leave Libya. He won't agree to that until his prospects for staying have been utterly eliminated, probably after his military commanders abandon him. We're far from that yet.
It's worth noting that in 1986, the U.S. acted basically alone. France, Spain and Italy all denied overflight permission for the raid, so the attacks had to be flown out of the UK through the straights of Gibraltar, with aerial refueling. The League of Arab States was outraged. Many bombs went astray, there were lots of civilian collateral casualties, and no regime change occurred. The raid was merely punitive, and many analysts suggest Gadaffi himself was ultimately helped, rather than harmed, by the raid.
Obama is acting wisely to proceed with more caution, to (hopefully) make this effort both more effective and less about the U.S. He's probably also wise to avoid extreme strategies like decapitation, both because they would backfire and because the specter of the U.S. assassinating world leaders is so disturbing, no matter how gross they are. The less this is about us, and the more is Gadaffi is left to the Libyans to deal with, the better. (He deserves a proper Chauchesku finish, IMHO, but I'm just an American, it's not up to me.)
And look at those women go! Hillary Clinton, Susan Rice and Samantha Power are the influences behind this response, according to the N.Y. Times yesterday. The men on the NSC argued against it!