When Sarah Palin decides regular English words aren't good enough, she'll just go ahead and make a new one. Here, Refudiate bridges the gap between "refuse" and "repudiate", to mean exactly what she wants it to mean.
"The President and his wife ... they can refudiate what this group (the NAACP) is saying." - Sarah Palin, on F-F-Fox News
When Twitter users decided that Sarah Palin was not, as she implied, the equivalent to a modern-day Shakespeare, they dutifully gave this term to describe what she probably didn't intend to describe.
Being when you make a mistake, use a word that doesn't exist, then try to claim that English is a "living language" where making up words is all good. It's not, really. We already have lots of really good words. Refudiate isn't one of them.