Obama the radical centrist
The "big lie" of greatest currency among conservatives is that Obama campaigned as a moderate but became a fire-breathing radical once he reached the Oval Office--for example, see Newt Gingrich's version:
I think [Obama] worked very hard at being a person who is normal, reasonable, moderate, bipartisan, transparent, accommodating - none of which was true.
Joshua Greenman analyzes this claim in the NY Daily News that Newt and the other conservatives are (big surprise!) lying:
Since taking office, the President has been remarkably consistent in doing what he said he would do. In fact, if he has veered at all, it's been by drifting toward the center or the right on issues dear to the Democratic base.
Greenman provides examples on issues ranging from healthcare to the economy, from Gitmo to gay rights, and from immigration to education. I doubt that conservatives could provide a coherent rebuttal--or, if they could, their list would likely be (like Newt) full of shit.
Marc Ambinder writes at The Atlantic that "Gingrich Is So Off, He's Not Even Wrong:"
It will be interesting for Gingrich to try to portray the President, who has sanctioned the expansion of CIA and special forces operations worldwide to hunt and kill anti-Western Islamic jihadists worldwide, as somehow blindly obeying a command by his unconsciousness to weaken America because he believes in socialism and in reducing America's power. [...] Newt Gingrich is an intensely smart man given to peregrinations of crazy. He can be a legitimate presidential candidate, or he can be a demagogue. For 2012, perhaps in this political climate, he is signaling that he is going to be both.
Daniel Larison's "Chasing Ghosts" at American Conservative observes that:
Obama made himself into the accommodating, establishmentarian, conventional politician and monogamous family man...as a complete repudiation of his father's life and political failures. People who insist on trying to see Obama as a left-wing radical, closeted or otherwise, will simply be chasing after ghosts and making themselves look inexcusably foolish in the process.
As long as the wingnuts keep getting TV invitations and book contracts, it doesn't appear that they care very much about looking inexcusably foolish.