Fearful of any type of conflict after two world wars devastated Europe, the Europeans love Obama because they are confident he won't ask them to do anything that might disturb their lovely cocoon that they live in (from Stratfor):
[The Europeans] love Obama because he took office promising to consult with them. They understood this promise in two ways. One was that in consulting the Europeans, Obama would give them veto power. Second, they understood him as being a president like Kennedy, namely, as one unwilling to take imprudent risks. How they remember Kennedy that way given the Bay of Pigs, the Cuban Missile Crisis and the coup against Diem in Vietnam is hard to fathom, but of course, many Americans remember him the same way. The Europeans compare Obama to an imaginary Kennedy, but what they really think is that he is another Clinton.
Clinton was Clinton because of the times he lived in and not because of his nature: The collapse of the Soviet Union created a peaceful interregnum in which Clinton didn’t need to make demands on Europe’s comfortable prosperity. George W. Bush lived in a different world, and that caused him to resume taking risks and making demands.
It's the veto power over our action they want. Multi-lateralism almost always means, for our European friends, a consensus to do nothing rather than joining us to take action. How else do you explain the ridiculous European report on the Russo-Georgian War of 2008?
I noted the European love for a president they believed would ask nothing of them. As I wrote in the former (with a bonus rant on Thomas Friedman!):
The Europeans count on Obama to never ask for anything. That's why they like him.
The really amazing thing is that the European elites don't just fear America dragging them into war. The European elites fear their own people will spark a war--the elites actually blame their own people for two world wars. That's why the elites will jam through the European Union treaty no matter what.
A funny sophisticated continent the Euros live in--they love our European president who they believe won't get them into war and they fear their own people who they believe are at heart war mongers.
Enjoy your dose of nuance.