If Canadians were being honest with themselves, they'd admit that socialized health care in this country is a myth. Our system is not a national one, it is governed by each province separately - the only "national" thing about Canadian health care is the financial assistance provided by the federal government ("assistance" being the operative word here - the feds only assist in the funding, they don't pay the whole thing). Even the terminology of Canadian health care -- "transfers" -- implies a decentralization of power from the centre to the edges. And, increasingly, private health care is creeping toward acceptance.
Tommy Douglas isn't the father of socialized medicare in Canada, he's the father of public health care in Saskatchewan, an idea that the other provinces, over time, appropriated, resulting in a web of provincial health plans that covers the entire country, but varies, often widely, from province to province.
A national health care plan, in theory, would offer the same level and quality of health care to every Canadian, via a central body. Our system isn't designed to do that: the Canada Health Act doesn't govern the ways in which health care is distributed, it only sets out broad guideline under which provinces qualify for funding of their individual health care mandates.
The problem, then, with the Harper government's announcement in December that it would tie health care funding to economic growth starting in 2018 isn't that doing so may destroy national medicare, it's that it will increase the inequity among provincial health plans.