According to popular belief, Sinclair Lewis, a Nobel-prize winning author of the early 20th century, wrote the above quote. That's probably because of his known political writings and views about the times in which he lived.
However, there appears to be no known proof that he actually said or wrote those exact words.
Nevertheless, he did write "It Can't Happen Here", a novel about how fascism might come to America, slowly seeping into the power positions of our government, until suddenly it was too late to turn things around. It's a chilling book, and probably the main reason why so many believe he is the source of the quote: "When fascism comes to America, it will be wrapped in the flag and carrying a cross."
If you get a chance to read the book, I HIGHLY recommend that you do. It seems as if the current situation in America is being acted out, play by play and bit by bit, according to the plot line of Lewis' book. Get it at your library, off of Amazon or you can even read it for free online.
Here's a link to Project Gutenberg's free online version: