To talk, in any real sense, of a multipolar world is to ignore the actual reality on the ground. America is still the top economy, the top military power, etc. But that's not America's point -- not to discuss the reality, but to understate America's power -- and in so doing, acknowledge that America is constrained by the rest of the world.
This newfound (rediscovered?) humility seems to be serving America well -- many allies and neutrals were sick to death of being bullied about and insulted. They see it in their own interest to reward America for it's good behavior. America, by being humble, gives the rest of the world back it's pride. Though intangible, it is something that diplomats appreciate -- and are motivated to respond to, in good measure.
Our enemies? They are uncertain, confused, and indecisive. America has much to offer them -- and now that she doesn't come with a baseball bat and brass knuckles, they are reappraising their approach. Each of America's enemies has many more priorities than simply "I hate America" (even Chavez!). And they all understand that America has the power to make or break their ambitions -- by favoring their enemies, if nothing else. Iran wants to be a regional power, rivaling Saudi Arabia or Egypt.