Because it's natural for a parent to feel defensive of their kids you could find yourself being painted as the bad guy and, hey presto, your relationship with their dad has just been undermined. On the other hand, the less of a reaction the child gets from you, the less 'payoff' there is. I realise that this is often easier said than done but you shouldn't react in a negative way. Be pleasant and fair with the child and you will eventually establish that you are not the enemy. Even if you really don't feel like it, be kind and concerned about her and make a point of praising her good points, but for God's sake don't try to mother her! That's probably what she's expecting and one of the things she is afraid of. Be approachable and be a friend but don't make her think you are trying to be her new mum.
Encourage her and her dad to have lots of cuddles and a bit of a laugh together. That should help to heal any insecurities she might have about you standing between her and her dad. I'm sure you aren't but she probably doesn't see it that way.
Ideally all this should eventually lead to a better relationship with the child and she would no longer see you as a threat who has taken daddy away from her. In the real world, If this is going to happen it takes a long time and copious amounts of patience is required.
It's getting a bit boring to hear these Super Nanny types keep banging on about it these days but, the old adage is true.....Ignore the bad behaviour and praise the good. It seems to work.
By the way, it's not personal! Your partner's daughter is behaving in a very typical way for a child who's parents have split and have new partners. If your partner was with someone else entirely they would be getting the same treatment you are.
Good luck and best wishes.
<I just wish I was good at taking my own advice! ;oP >