Sometimes, you can start out your story with a main character who has unpleasant elements to their personality, but a character must be likable or, at the very least, relatable for the reader. Here are ways to show more than the prickly outer elements of her personality.
If you give the main character a worthy goal in the first pages of the novel, then you give yourself time to make a seemingly unlikable character grow on the reader.
By worthy, I mean something the reader will want that character to succeed at–- rescuing children, helping a nice person find happiness, etc. Even if the character starts out doing it for a base reason like money, the reader will still want him to succeed.
Simple things can help make a character start to grow on the reader. Pets are always a good option. Either he has one, or he can't resist the heroine's kitten, or something like that. Having him interact positively with a child is also a good likability quickie.
Recently, I read a short story in which the heroine breaks into the apartment of a possible villain-- a hard-ass security agent. A teddy bear is sitting on his couch, and he later admits it belongs to his nephew. With that simple stroke, the author made a seemingly unlikable bad guy a much nicer person.
Giving a character a vulnerability that the reader can relate to is also a good likability quickie. It can be as simple as a chick lit heroine having a bad hair day and the boss from heck, or the bad ass hero getting into a small plane and freaking out because he finds a snake.
Eventually, more likable elements of that character's personality will have to be shown, though, so the bad parts of her personality don't overwhelm the reader.
In some genre fiction like thrillers, the immediate likability quotient doesn't have to be high at the beginning, particularly if the character is strong and effective in what he needs to do.
But in a romance, the hero or heroine should be likable from the very beginning. The other main character can become likable as the book progresses, but he should not start as totally horrible. Some character traits like cruelty can't be forgiven or changed because, in real life, they never are.