Anger at the war in Iraq contributed to this week's crushing defeat of Bush's Republican party in mid-term elections for the House of Representatives and Congress.
Australia has about 1,500 troops in and around Iraq and, according to recent opinion polls, almost two in three Australians want these forces brought home.
"George W. Bush is captain of a sinking political ship. The message for Australia is to beware being caught supporting policies that will sink with Bush," wrote national affairs commentator Paul Kelly in the daily Australian newspaper.
Greens Senator Bob Brown described the Democrats' victory as an anti-war rebuke to Bush and warned Howard he could be next.
"Australian voters oppose the war in increasing droves. The 2006 US voter backlash will become the 2007 Aussie voter backlash on Iraq," he said.
Australia was one of the first nations to commit troops to the 2003 US-led war that toppled Saddam Hussein. Howard wants the troops to stay until Iraq can handle its own security, but the Labour opposition says it will bring them home if elected.
Legislative elections are due to be held by the end of 2007.

TIME FOR CHANGE?
Labour leader Kim Beazley said the anti-Iraq sentiments of American voters were shared by many Australians.
"There is a real hunger in the American community for a change in strategy on Iraq and for effective action from the President to bring this conflict to a conclusion," Beazley told Australian television.
"I don't think the Australian people are any different from that. They think this (Iraq war) is a profound mistake which has not made them more secure and they want to see their political leaders working to conclude it."
Opinion polls show Labor is making inroads on Howard, whose 10-year grip on power has been loosened by rising interest rates and fuel prices which have hurt the middle-class voters the conservative prime minister calls his "battlers".
But Howard has an uncanny knack of sensing the public mood, an ability that has helped him win four straight elections.
While Bush is now offering words of conciliation over Iraq, Howard on the other hand is standing firm, saying he would urge Bush to stay the course in Iraq.
He told local radio on Friday he believed most Australians would not want him to pull troops out of Iraq now.
"They do recognise and accept that if the coalition leaves Iraq in circumstances which is seen as a defeat that would be incredibly bad for American authority and that in turn would be very bad for Australia," Howard said.
Unlike Bush or British Prime Minister Tony Blair, another staunch US ally, Howard is the only leader seeking re-election.
The Sydney Morning Herald newspaper ran an opinion piece on the US elections and Howard, with a cartoon showing the prime minister in uniform proudly marching past a bowed Bush.
"If Bush is showing contrition, you'll see no such thing from John Howard," wrote Peter Hartcher.

Copyright Reuters, 2006