I am very resistant to the idea that a character simply cannot be sarcastic and likable at the same time. (Not just because that would invalidate, like, my whole personal persona, though that is obviously a factor! ;-))
So I'm trying to figure out: what makes you like a character? When you're reading a book, what makes you decide to care about what happens to the protagonist? What character traits make you want to throw the book into your nearest toilet?
You don't actually have to be a literature person to answer this. I'm asking anyone who's ever read a book.