Mr Harper has been in office since January 2006
Opposition parties in Canada have joined forces to try to topple the minority Conservative government less than two months after elections.
The Liberals, New Democrats and Bloc Quebecois say the government is failing to tackle Canada's economic problems.
They intend to use their joint majority to vote against PM Stephen Harper in a confidence motion due next Monday.
If Mr Harper loses, Canada's Governor General would call a snap poll or ask the opposition to form the government.
Constitutional experts say Governor General Michaelle Jean may favour the second option as the country has had an election so recently.
Mr Harper's Conservatives were re-elected in October but as they failed to secure a majority, they must rely on the support of the opposition to pass budgets and laws.
The prime minister could try to ride his luck and let the confidence vote go ahead on 8 December, or he could try to stave off defeat by asking the Governor General to suspend parliament until 27 January when the government is set to table its budget.
Either way, Mr Harper faces a difficult choice and his worst crisis since first winning power in January 2006, analysts say.
The opposition Liberals and New Democrats signed a formal agreement to form a coalition that would govern until 30 June 2010 and have the tacit support of the separatist Bloc Quebecois.
The new prime minister would be the Liberal leader, Stephane Dion, who led his party to a serious defeat in the 14 October polls and had already announced plans to step down next May.
The opposition parties say they were spurred to action by the failure of the government to deal with the financial crisis and boost the country's economy, and that they are set to introduce a stimulus package.
Governor General Michaelle Jean's post is usually largely ceremonial
"Given the critical situation facing our fellow citizens and the refusal and inability of the Harper government to deal with this critical situation, the opposition parties have decided that it was now time to take action," Mr Dion said.
The opposition parties were also angered by Mr Harper's attempt to eliminate public financing of political parties, a move that would hit them hard, Reuters reports.
Mr Harper said the Liberal leader had done "a deal with the separatists in order to get the power the voters denied him at the ballot box" and described the opposition's move as an "undemocratic" power grab.