The Conservative government wants to see a vote on extending the Afghanistan mission happen one week from Thursday.
CTV's Graham Richardson told Canada AM that a government source told him the debate will end by March 13, with a vote happening that day.
The motion calls for Canada's mission in Afghanistan to continue until July 2011, contingent on NATO supplying another 1,000 troops plus some equipment like helicopters to help Canada in Kandahar province.
Richardson said one unresolved issue for the Liberals is whether the 1,000 troops will replace the Canadian battle group, freeing those troops up to do other work.
There are a total of 2,500 Canadian troops in Kandahar province. A Canadian soldier died in a roadside bomb blast on Sunday, the 79th to die in Afghanistan since 2002.
Richardson noted the differences between the Conservatives and Liberals on extending the mission have largely been smoothed over. The motion, for example, provides for a firm end date.
The Liberals have suggested they will support the motion if the government answers a few questions.
However, the NDP and Bloc Quebecois are likely to oppose the motion.
The Liberals want Canadian soldiers to focus more on reconstruction and training the Afghan army rather than engage the Taliban in combat.
Last week, Defence Minister Peter MacKay said there will be times after February 2009 -- the current scheduled end date to the mission -- that Canadian troops will have to be involved in combat.
Finding the additional 1,000 troops -- a key recommendation of the Manley panel on the mission's future -- has been problematic. Very few NATO countries have expressing willingness to send troops to Kandahar, possibly the most violent province in Afghanistan.
U.S. President George Bush signalled last week that he might provide the extra troops.
The U.S. will be also sending 3,200 Marines to southern Afghanistan for a seven-month tour starting this April.
At a weekend news conference at his ranch in Crawford, Texas, Bush said he would be pushing NATO countries to contribute more when a key meeting is held in Bucharest, Romania next month.
"As you know, my administration has made it abundantly clear, we expect people to ... carry a heavy burden if they're going to be in Afghanistan. In other words, (Defense) Secretary (Robert) Gates said, 'look, if we're going to fight as an alliance, let's fight as an alliance'," Bush said.
"Having said that, I understand there's certain political constraints on certain countries. ... I am going to go to Bucharest with the notion that we're thankful for the contributions being made, and encourage people to contribute more. ... We are trying to help Canada realize her goal of 1,000 additional fighters in the southern part of the country, as is Anders working toward that."
Bush was referring to Denmark's Prime Minister Anders Rasmussen, who was visiting the ranch. Denmark has 550 troops serving in Afghanistan.