There are only two possibilities, to my mind:
(1) The similarity is unintentional. The Obama logo combines a familiar symbol for doctors/medical care along with the classic "Obama logo" from the 2008 campaign. It's just similar shapes.
(2) The similarity is intentional, and Obama is a Shadow Nazi. He's stupidly revealing to us his actual, dark intentions, via the use of logos, and Rush Limbaugh's the only American savvy enough to put the pieces together, sort of like a paranoia-and-Oxycontin-fueled, obese version of Tom Hanks in the "Da Vinci Code."
Can't really decide, though...Both options seem so plausible.