No member of parliament wants to open the Canadian Constitution for any reason nor will they.  If you want to know why just examine the Charlottetown Accord, which Canadians rejected.  The reason that the Federal Government has any say in health care at all is that they promised to fund 50% of the present system.  That eroded over time.  Money keeps the PM in the game.  Without money for the Provinces for health care, the Premiers could tell the PM to get lost and Constitutionally they would be right.