Agreed. I can believe that many newspapers are lax in verifying letter writers. But to believe that "Ellie Light" got "her" letter published in so many dozens of papers in a period of 2 weeks--in their entirety, intact--is just silly.
The first appearance of this letter appears to be Jan 7, when Politico Editor Ben Smith ran it with a preface (emphasis mine): "I get a lot of unsolicited e-mail and should probably publish more of it; this defense of Obama, sent in by someone named Ellie Light, seemed to crystallize a point his supporters have been trying to make for a while:"
Strange choice of words by an editor. But it's the exact sort of weasel-wording a dishonest editor would use to conceal his knowledge of who did write it.