Canadian Conservatives prefer relatively pro-market policies. Quebec is the most statist province in the country and its political influence drives Canada's economic policies well to the left of where they would be in a separate anglophone Canada. Canadian Conservatives hate paying for federal government subsidies to Quebec (Quebec is a major net recipient of transfer payments from the federal government). Obviously, there would be no such subsidies if Quebec were an independent nation. In the long run, secession might even lead to relatively more market-oriented policies within Quebec itself, since an independent Quebec government could no longer rely on Ottawa transfer payments to finance its statism. Finally, Quebec secession would be a major political boon for the Conservative Party. In the recent election, the Conservatives won 133 of 233 parliament seats in the anglophone provinces, but only 10 of 75 in Quebec. The Tories won't necessarily do this well in the "rest of Canada" every time; but their odds of getting a majority would be greatly improved if Quebec were to secede.
One of the readers at the Volokh conspiracy answers Ilya's question by saying:
Being a "federalist" party in the Canadian sense (that is, anti-secessionist) is the sine qua non for support in English Canada. There might be some number of western voters who would cheer Quebec's departure and be happy that the ideological median in their new country had moved a long way right. But the Conservatives would sacrifice something close to all their votes in Ontario (the largest province)-- many of whom have no identity-commitment to being Conservative but have a massive investment in the idea of Canada.... Ontario is far from solidly conservative or culturally conservative, and it would electorally cut off at the knees any party that abandoned federalism. Whatever Conservative leaders might wish in their hearts, it's a political non-starter.
How about America, Canada, Conservatives and Liberals come together and give everybody a little of what they want? Quebec gets its own nation. Liberals get a nation made up of the following Canadian provinces and American states: Ontario, Newfoundland and Labradour, Prince Edward Island, Nova Scotia, New Brunswick, Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, Connecticut, New York, New Jersey, Delaware, Maryland, Washington, DC, Pennsylvania, Michigan, Minnesota, Wisconsin, Illinois, Iowa, California, Washington, Oregon, and Hawaii. Conservative get a nation made up of the following Canadian provinces and American states: Alaska, Yukon Territories, Northwest Territories, Nunavet, Manitoba, Saskatchewan, Alberta, British Columbia, Idaho, Montana, North Dakota, South Dakota, Wyoming, Utah, Arizona, Nebraska, Kansas, Oklahoma, Texas, Arkansas, Louisiana, Mississippi, Alabama, Georgia, South Carolina, Tennessee and Kentucky. The following American states would go with whatever nation they prefer to join: Nevada, Colorado, New Mexico, Florida, North Carolina, Virginia, West Virginia, Ohio, Indiana, and Missouri.
I know it is not going to happen, but it would be a solution that should leave everybody better off.