But Australia was one of the four coalition nations that took part in the invasion of Iraq, and in US eyes an Australian withdrawal would have much greater symbolic weight than the Spanish withdrawal; it could be interpreted as heralding a collapse of will among Washington's closest allies.
http://theage.com.au/articles/2004/06/14/1087065079061.html

The US would send a dangerous signal to the world if it refused to accept the result of an election in a longstanding ally.

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http://theage.com.au/articles/2004/06/14/1087065079793.html
The Bush Administration fears the symbolism could be devastating on two levels.

First, the timing of any decision by an incoming Labor government could prove awkward in the extreme for Bush as he mounts his campaign for re-election in November. Given Bush's Democratic rival, John Kerry, has built his critique of Bush's foreign policy on the premise that the President has proved incapable of attracting broad international support for the war on terror, the likely political impact of Australia abandoning the coalition is not hard to imagine.

But the more profound concern is the potentially cancerous effect on America's capacity to strengthen and sustain as broad as possible a coalition for its tough agenda, not only in Iraq but in the wider campaign against Islamist terrorism. The Bush Administration is apprehensive (a sentiment shared, as it happens, by some senior Democrats) that a unilateral withdrawal by Australia would represent a resounding vote of no confidence in US global strategy.

However, to presume this or any other American administration would junk the alliance on this issue - on this issue alone - is ludicrous. For a start, it would mean the US effectively repudiating the outcome of an election in one of the world's oldest democracies, a nation that also happens to be one of America's longest-standing friends and allies.