"But one hears that healthy young adults are having to wait 2-3 years to be assigned a doctor..."
That's just wrong. Canadians are not "assigned" doctors by the gov't. In fact they're freer to choose their doctors than Americans on PPOs. Doctors do not work for the gov't.
Though this is slightly out of date (Canadians can purchase secondary insurance and services now I believe) Ezra Klein's piece on the Canadian System is good.
Canada care is unapologetic, no-holds-barred single-payer. The single-payer, by the way, is not Canada as a whole, but each specific province, so it's not quite as monolithic as we think. It's financed by taxes, but the taxes vary from province to province, so there is a certain amount of variation in how the system pays its bills...
Care varies only according to province (and, assumedly, individual doctors and hospitals), not according to class. Interestingly, low-income Canadians actually receive more care than do the affluent, owing to the higher rates of disease in poorer communities...
In 1970, the year before Canada's health care system came online, Canada and the US spent about the same on health care, 7.2% and 7.4% of GDP respectively. By 1990, it was 9% and 11.9%. And by 2002, it was 9.6% and 14.6%. So while our health care spending shot up by 7.6% of GDP and still doesn't cover out citizenry, theirs had a 4.5% climb and got everyone in the goddamn country covered (remember: the first number is pre-universal health insurance)...
In any case, Canada's got some problems. Wait times for elective surgeries can suck real bad and, according to an LA Times article from April 10th, some folks do cross the border to speed things up. But vital procedures are done quicker and, amazingly, any Canadian can get any necessary surgery done that they want. If elective, it may take some time, but there's never a question over whether they'll be treated.
Here's a Canadian Gov't description of their system.
Canada's health care system has been a work in progress since its inception. Reforms have been made over the past four decades and will continue in response to changes within medicine and throughout society. The basics, however, remain the same - universal coverage for medically necessary health care services provided on the basis of need, rather than the ability to pay...
When Canadians need health care, they generally contact a primary health care professional, who could be a family doctor, nurse, nurse practitioner, physiotherapist, pharmacist, etc., often working in a team of health care professionals. Services provided at the first point of contact with the health care system are known as primary health care services and they form the foundation of the health care system.... Most doctors work in independent or group practices, and are not employed by the government. Some work in community health centres, hospital-based group practices, primary health care teams or are affiliated with hospital out-patient departments...
Many Canadians, either through their employers or on their own, are covered by private health insurance and the level of service provided varies according to the plan purchased...
Canada's labour costs are lower because employers do not have to fully fund employee health benefits; this gives businesses in Canada a competitive edge. The annual KPMG competitiveness report, which compares business costs in several industrialized countries, continues to find that Canada has lower business costs than the US, and the lowest total labour costs of the countries compared.
Canada stacks up pretty well in international comparisons. It is not socialized health care, it is a single payer insurance plan. It's not perfect, no system is, but it's not the nightmare that conservatives try to make it out to be. Speaking on an anecdotal level, my wife's step-father had heart trouble while visiting Canada and received treatment superior to what he got in his hometown hospital.