Do you know how screwed we'd be if every country had their own Dick Cheney?
Imagine the run-up to the invasion. The US presents it's case, and France disagrees. The US says, we'll go it alone if we have to, and Cheney-France says, "Fine. Help yourself." At the Security Council vote, Cheney-Germany and Cheney-France say "It's not in our interest to vote for your invasion, and you said you don't need our approval anyway" and deliver a veto each. Cheney-Russia decides to abstain while Cheney-China suggests the two vetoes mean there's no point in continuing the voting.
Cheney-USA invades and punks Cheney-Iraq. Insurgence proceeds, the USofA asks for help and all the Cheneys around the world say, "Sure. At cost plus percentage, and you don't get to audit our books."
See, when the USofA started that "we will go it alone if we have to" crap, they never expected to go it alone. They expected others to feel compelled (by economic necessity if nothing else), to be pulled along in their wake, as it were. And it might happen here.
But a world of Cheneys would recognize that the USofA was tying itself down militarily, economically and politically (international politics) in ways that, without help from the other major players, it can not support.