We could debate the meaning of Socialism all day long, but it's tenants remain the same from the etymology of the word. You have
social which comes to us basically from the old meaning of social which was Middle French social and Latin socialis. I'll let others dig that back as far as they want to go, but the original meaning of the word is in the sense of society. Around the middle of the 19th century to the turn of last century, the word social in the more modern sense came to be and then we had Socialism. (-ism is a state of being, doctrine, etc.)
The idea of socialism is simply that society owns the means of production. It's distinguished from Communism in that Socialism is on the way to Communism in Marxist theory and it basically refers to a stronger government control as opposed to the communal system. The problem with this distinction is that governments tend to control as much as they can, hence the reason Communism failed - far quicker than other forms of government. Names don't always hide the truth, though. Socialism is simplified to be when the government controls production and distribution - this can be healthcare, this can be nation utilities, etc.
The American theory (at least the original one) for government is that it steps in only at the last moment when nothing else works. Think of it as a last-ditch safety net which is not used all too often. Unfortunately, in modern times, this paradigm has shifted. We like convenience and it makes sense that most societies like to superficially place their cares on others.
To argue that universal healthcare (in Canada, for example 70% is public ownership) is not socialist...well that's a bad argument from the get-go. The very meaning of the word Socialism defines the state of public healthcare. If society owns it (IE: pays for it), that's Socialism.
These changes tend to creep rather than come overnight in revolutions these days. Like it or not, each industry and service that the government takes on moves it closer to socialism by definition. Social security, Medicare, Medicaid, etc. are all programs that do just that. I don't dispute that and I think that proves the overall point of this thread. Personally, I'd rather have those few thousand dollars each year that come out of my paycheck for social security to invest privately for my future and retirement. I could easily make a much better gain than our government, because it's effectively a ponzi scheme - but that's another argument for another day.
I think this is the linchpin. The US is structured differently as you said, and there are far more people. If they are increasing your taxes so dramatically then maybe the govt should be listening to the people on the street and taking some time to work out a better system that's not going to burden the common man so much.
That's the problem, look at how Medicaid and Medicare have been run - which are microcosms of universal healthcare (and as large as some countries that have universal care I might add). We've raked up unfunded liabilities for more than all the money in the world already. We're talking well over $100 trillion!
(One Trillion Seconds = 31,688 Years, 269 Days, 1 Hour, 46 Minutes, 40 Seconds for a little perspective.)
The problem with this bill is now the government has entered into the arena of telling you what you can and cannot do. We must buy healthcare, otherwise you're penalized. The problem with that is that the people who don't buy it generally cannot afford it. Yes there are subsidies, but come to America sometime and watch subsidies work. And that goes to what Martin says - the largest single danger is that now the government can regulate anything. Look up the commerce clause of the Constitution here in the US. They've now expanded that you not only regulating what you buy when you buy it, but now they can regulate what you buy and tell you to purchase something. This is done with cars of course already (car insurance), but you're not born with an inherent right to drive.
This discussion does not even consider illegal immigration, which will be the next focus after the interlude of financial reform.