Common name-calling from the right about Barack Obama has been that he is like Adolf Hitler or that he's a nazi or a fascist. Comparisons with Adolf Hitler have been based on the comparison that both are charismatic leaders and the perception among conservatives that Obama wants to take away this country's freedom. In the U.S. system of electoral politics, charisma is almost a necessary precondition to becoming president. The majority of Americans want a president they can feel inspired by, confident in, or relate to (e.g., the perception that George W. Bush is a man they would feel comfortable having a beer with or inviting to a backyard barbecue with the family). Former vice president Al Gore and Senator John Kerry were hammered by the media for appearing too wonkish and wooden. Former president Ronald Reagan was considered highly charismatic, "the Great Communicator" whose ideas still influence the Republican Party today.
The second attack is that Barack Obama wants to take away America's freedom. This is of course an ideological consideration. The Right tends to consider the existence of government itself an impingement on freedom rather than perhaps a guarantor of freedom, any form of taxation (except in support of the military) as a form of theft, and any regulation of commerce and industry as communism. The current hysteria is that healthcare reform, especially any public option, is a slight against freedom. The connection is an emotional one but not a logical one. The connection is a visceral association between economic freedom and socialism and between socialism and destruction of freedom. There is no consideration of the freedom healthcare reform would give to the uninsured or underinsured. There is no consideration that some regulation can actually prevent things like monopolies and consumer fraud/abuse that are destructive of people's freedom.
The assertion that Obama is a nazi or fascist implies that Obama follows certain totalitarian or authoritarian right-wing policies.The only policy that resembles fascism I have noted is a corporatist policy of bailing out "too-big-to-fail" banks and other financial institutions, GM, etc. The rest of the package from National Socialism, Fascism, the Falange, and Ba'athists bears little resemblance to contemporary Democratic policy: racial/national purity, xenophobia and strong anti-immigration policies, removal/ostracism of dissident/radical elements from society, military aggression, absolute submission to the state, an alliance between the state and traditional authorities (the military, the church, the nobility), and suspension of democratic rights. Actually, we saw more of those things during the Bush administration, and Obama has been trying to reverse many of those policies now.