Socialism is on the opposite end of the political spectrum of Fascism. Nazism is fascism. That Hitler named his party the National Socialist Party shows how popular and widespread socialist ideas were amongst the working masses of Germany at the time.
But Obamacare is not socialist in the least bit. There are different varieties of socialism.
Bourgeois socialism aims to pass measures that will subdue the anger of the toiling masses without endangering the capitalist system itself. Bourgeois socialism is practiced to greater and lesser degrees (depending on how strong and angry the toilers are) in Western Europe and Canada.
National socialism aims to prevent the working class from coming to power when the capitalist class is unable or unwilling to rule. It comes in two forms. The first is "real existing socialism" as existed in the USSR, the Eastern Bloc, Yugoslavia, China, and continues to exist in North Korea today. The means of production are taken into state ownership and administered by middle class bureaucrats. The second form of national socialism is fascism. Fascism arises when the capitalist class in rendered unable to rule. Rather than trying to rule themselves and eventually failing (as real existing socialism always does), the middle classes join in a ruling bloc with the capitalist class, helping to prop up their rule and system through a form of super capitalism. They turn democracy on its head, with corporate powers ruling society through their control of a massive state apparatus staffed by middle class bureaucrats. Fascism existed in Germany, Italy, Spain, Chile and a few other countries.
Proletarian socialism has sprung up a few times, only to be smashed to bits by capitalist governments and counterrevolution. It existed during the Paris Commune (1871), the St. Louis Commune (1877), the Bavarian revolution in Germany (1919), the Shanghai Commune (1925), the Spanish revolution (1936), May in France (1968), the Hungarian Revolution (1956), and in the early stages of the October Revolution in the Russian Empire (1917). Proletarian socialism aims to eliminate classes and wage slavery on a world scale through working class revolution and the replacement of private ownership of the means of production with public ownership and democratic control of industry.
There are other branches of socialism (feudal socialism, clerical socialism, etc.), but none are relevant to this discussion.
That said, Obamacare is a corporatist measure, not a socialist measure of any kind. Whereas socialized healthcare is a state controlled system, Obamacare is simply an attempt to taking the burden of paying for healthcare off of capitalist employers while simultaneously pumping more money into the private insurance giants by forcing everyone to take out a policy. This follows the model of Japan and South Korea.
Obamacare with neither destroy or preserve the system that exists in the US. It's simply an attempt by a certain section of the ruling class to "perfect" its rule. Every single industrialized country and many developing countries have some form of universal healthcare (including those that are much stronger economically than the US). See map:
http://upload.wikimedia.org/wikipedia/en/e/e7/Universal_Health_Care_World_Map.svg
The countries that don't have universal insurance are in the poorest parts of the world: Africa, Central America, the Caribbean, the Near East and Southeast Asia.
Besides, the US government already pays about 60% of healthcare costs in this country.
In order for real socialized medical coverage, in which anyone would be able to work into any public hospital anywhere and receive care with no questions or money asked, to come into being here, we'd have to dismantle the insurance giants all together. That kind of thing won't come from either of the two major parties, which are tied by thousands of strings to the insurance corporations.