That is a massively incorrect statement, which pops up every time government-mandated healthcare debates appear, which I wish to squash ASAP: http://en.wikipedia.org/wiki/Socialism

Universal healthcare != socialism. Not even remotely. It's a political mud-slinging attempt to equate healthcare changes with the historical fear of the USSR that seems to have infected far more people than it should even have reached. Yes, fear the Reds, they'll lob bombs at you now that the cold war is over. They've just been waiting.

At the absolute closest would be if the government were to run all the healthcare directly (it's not - there are and will be many private healthcare markets), and then it would be a socialist action, not socialism (a socialist government).

To make matters worse for this use, any form of taxation can be described as a socialist action. That doesn't make any government that taxes its citizens a socialist government.