As per Asfriend's request.
Honestly, since I do not personally know the man, I don't know with 100% certainty if he is or isn't a socialist. He very well could be. But then that would make him an even bigger hypocrite than he already is. For a politician.
So here we go.
Socialism refers to a broad set of economic theories of social organization advocating state or collective ownership and administration of the means of production and distribution of goods, and the creation of an egalitarian society. Modern socialism originated in the late nineteenth-century working class. Karl Marx posited that socialism would be achieved via class struggle and a proletarian revolution, it being the transitional stage between capitalism and communism.
It should be noted that Barack Obama has repeatedly stated that the wealthy need to pay more in taxes (higher rate) than the middle class, an opinion that John McCain shared as well during the 2008 campaign. It could be argued that this is a form of "class warfare" (I hate using this phrase because it cheapens what war really truly is.) pitting the middle class against the upper class. President Obama's tax plan and Senator McCain's tax plan involved tax credits that would give money to those who pay no federal income taxes (these individuals still pay FICA taxes, sales taxes, state income taxes (where applicable) and excise taxes).
Class warfare is a very vague term and has been over used. Along with the "war on women/poverty/drugs/Christmas". Complaining about the increasing plight and contraction of the middle class is not a feature of Marxist criticism. Marx viewed the middle-classes (bourgeois) as in coalition with older aristocratic and privileged classes against the producers (workers). Marx was all about the people at the bottom of the totem pole. Obama (along with most politicians) tend to cow tow to the middle class for votes since the middle class does tend to vote more than the poor and working class.
Also Marxism requires allegiance to some form of dialectical (this is an academic word meaning that there are connections between different things on different levels, such as interconnecting oppression) materialist understanding of history. In this view, all society is in a struggle for control of the social surplus and its use. This conflict cannot be ended until a revolution brings those who produce the material needs of society into control of that society. This is why reforms that merely reinforce capitalist divisions of society into laborers, owners, and managers cannot be viewed as Marxist. Marxist was all about the working class rising up with weapons and using it against the upper classes. To force them through violence to share the resources that came through their labor. I personally am a pacifist and I do not think this is necessary. One time I was part of a socialist group at my school and one of the members said that a violent revolution was the only way any of their ideas could be achieved. I left that group and never went back. I will never take part in committing physical violence against another person. That's not who I am.
To my knowledge, and correct me if I am wrong, President Obama has ever claimed that workers must be allowed take control of factories and begin directing production towards the real needs of society as a whole. Or that property and capital is the root cause for division and inequality in America. If he did, that would make him a Marxist.
Also, at the beginning of this post I gave a standard definition of Socialism. However, that's not the case for all socialists. I personally do not completely ascribe to Marx. Many Socialists do. He had some really good ideas but I could never bring myself to consider armed conflict as a viable option to change our society for the better. If anything, it would make it so much worse. The socialist group I belonged to at my school before I became part of the Democratic Socialists of Chicago had sever issues with another socialist group called The Socialist Vanguard. To the point where actual fights broke out when the two groups would attend protests. I never really understood why there was such animosity. Also, a great deal of socialist beliefs stem from solidarity. To support each other. To be there for each other enmass. That we are all in this together and we're all willing to do what it takes to make this world a better place for the poorest of the poor and the marginalized and exploited workers. Getting into fights with other socialist groups for whatever reason seemed counter intuitive. *sigh*
So, that's my own opinion on why Obama is not a socialist. I'll never know for sure though, since I'll probably never get to know him well enough to find out for sure how he personally feels.