Okay, so Sarah herself didn't actually say that, but an aide speaking on the good lady's behalf did. Palin's spokeswoman, Rebecca Mansour, at first claimed that Jon Stewart had never invited Palin onto the show (he's done so many times, all of which are recorded on television, most recently on January 18). She also claimed that Palin wouldn't make the appearance because she didn't want to boost his ratings (which, she would. Don't lie. Everyone in America would watch that).
She also defended the former governor from allegations of cowardice:
"She's not afraid of his show. She doesn't think about him all that much. Neither do I. However, I do recall that he's been rather vicious in his coverage of her, so I'm not sure why she would even want to appear on his show to give him a ratings boost. If you continue to imply that she's afraid of appearing on a comedian's satire news show, then you're just plain wrong. She's stared down big oil companies and won. Jon Stewart isn't all that intimidating."
Stewart has had some very good luck getting conservatives onto his show — and he's usually pretty nice to them. Donald Rumsfeld called his Daily Show interview "one of the most thoughtful" on his entire book tour. However, Palin's aide's bravado aside, there are very obvious reasons why she won't go on the show. As the Huffington Post wisely notes — this is a woman who got seriously tripped up by Katie goddamn Couric.