However he has repeatedly said that votes on such matters should be free votes, and any member—including a Harper stalwart—can propose such a measure. Harper himself wouldn't have to spend a minute on it, and it still could get the dirty deed done.
Just remember, that 'majority' got the votes of less than half the people. The Harper landslide—after almost five years of showing us what a great government he can lead—amounted to only about 3% more votes than his last useless election. But don't expect him now to start governing with the majority's needs and concerns in mind.
If a free vote outlaws abortion, brings back the death penalty, or makes gay marriage impossible … oh well.