Let's ignore for a moment that, for his entire presidential run, opponents of Barack Obama called him a socialist and now they call him a Nazi, two ideological positions that are literally on opposite ends of the political spectrum. Since such people are still also claiming "Obamacare" will turn the United States into "Russia" or "a socialized state," I think we ought to take a moment and think about the relationship between Obama (and other Democrats) and socialism.
I will here refute the claim that any Democrats are socialists. I also make the claim that Democrats (and indeed, everyone else) should become socialists, because socialism is good.
First, it's important to be clear: socialism does not mean "state run." The police are entirely state run, but nobody is complaining about "socialized police." The military is totally state run; no sane conservatives want to privatize the Marine Corps. Socialism is an economic concept that doesn't necessarily have anything to do with government at all.
Socialism has been many things over the years, but in all of its modern forms it stems from the basic observation that under capitalism, workers do not get the product of their labor. The product is owned by someone else, who then pays some fraction of the money made off of it back to the people who actually made (or did, in the case of services) it.
The one thing all serious forms of socialism have in common is the idea that people ought not to work "for" someone else, but may work "with" them. An absolute minimal socialist position would require worker, community, or state ownership of productive enterprises. In modern democratic countries, that is typically expressed as nationalizing the major industries and monopolies for the benefit of all, and switching smaller companies to worker-owned co-ops for the benefit of the workers. Again, this is pretty much a minimal requirement for socialism. It has nothing to do directly with universal health care or social welfare programs, or anything but workers controlling the product of their work rather than absent owners or stockholders who contribute nothing but permission to use their property. Socialist businesses may operate in a market, but the profit goes to the workers or to the public (depending on the system). It does not go to private investors or CEOs.
So we can see that no Democrat has ever proposed anything resembling a socialist proposal in Congress, on the topic of health care or anything else. There are no bills calling for the abolition of private capital investment banks, no opposition to the stock market. I have never heard the words "surplus value" uttered on the Senate floor. There are actually Democrats who are members of the Democratic Socialists of America, but they've never proposed anything exclusively socialist so it matters little.
"Socialist" health care would be more than a public option. "Socialist" health care would be more even than a single-payer system. "Socialist" health care would require that all hospitals, pharmacies, pharmaceutical companies, and other medical enterprises be owned by the state, the community they reside in, or even the very doctors, nurses, and other staff who work at them. Such enterprises would distribute all "profits" to the people who earned them, rather than to stockholders and executives. It would be a fully public system provided to all residents free at the point of delivery, not public insurance, and certainly not optional public insurance.
Even in a "best case" outcome of the current health care debate we are left with a system in which private insurance corporations inject themselves as parasites. Think about it for a second: private insurance doesn't actually do anything to earn its profit. Just as investors in corporations don't do anything to earn interest, nor do landlords do anything to earn their rents. Capitalism allows a class of people to earn money simply by making money available — it gives people money for nothing more than the privilege of already having enough money to spare. We don't need insurance. We need medical care, and there is no reason we can't collectively provide it for ourselves without middlemen. That's socialism.