I don't believe that NATO is dead. After the EU fails to build up a believable military reaction-force, NATO will be stronger than ever.
Europe needs USA and USA needs Europe. Europe needs USA more than USA needs Europe, but it's still a practical marriage that's going to last.
If not, Europe is toast...
Sorry, but this is just wishful thinking. SuziQ got it right - the really frightening threats for the European public are gone. The cold war is over and danger of terrorism is underestimated on the old continent. NATO is simply not needed anymore in their eyes, since wars like Iraq are for sure not seen as European business. Defense is something were money can be saved.
Besides - this way of thinking has its "justification" if we see it soley from the European point of view. There is indeed no direct classical millitary danger anymore. It is rather unlikely that the ChiComs or the Russians will do any attacks on Europe in the near future. Dangerous countries like Belarus could be overrunned easily with the rest of the cold-war armament if it should be nessecary. But this is also not probable. The only reason for a well equipped millitary are actions on the side of the Americans who engage themselves nearly everywhere.
People who think like that (and that are most of Europe) forget that i.e. guys like Hitler have to be eliminated. Yesterday, today and in the future. This makes NATO and millitary nessecary. Maybe the Americans did not find substancial amounts of WMDs, but they brought Saddam to justice and killed his evil sons. Only this was worth the effort.
We will see what the future brings, but I predict that the relation between America and Europe will loosen a bit. This does not have to be a disaster since both sides know that they are indeed depenent on each other. A strong connection will remain.