Social conservatism isn't the liability that the "experts" think it is.  Although the media is unified in its 100% unanimity on those issues, and generates hysteria, these are very secondary issues to most Canadians. As Harper showed, a clear, simple position on social issues easily cuts through the media hysteria. 
Paul Martin, the PM who passed ssm in 2005 lost the next election shortly after- and the politician that promised a re-do on that vote, S. Harper, won the next election. And Paul Martin's promise to do away with the "not-withstanding-clause" fell flat. 
Here in Ontario, no politician has ever done more for "progressive" values than premier Wynn, and she has the lowest poll rating in recent memory.
Canadians vote with their wallets. They also like their social programs. Threats to pensions, medicare, school systems etc, are much more alarming for voters.
The left wins when it promises to keep or solidify social programs.