My 3 year old daughter is very mean to my husband. She often tells him, "Don't talk to me". Also rarely wants to be by him until he is upset and goes to work. He has not done anything to her except be an excellent father. I'm not sure what to do to get her to change her ways.

How much interaction between just the two of them is there? Is he her biological father? If not, how long has he been in the picture? Does he spend one-on-one time with her? Does he have any of the childcare responsibilities with her... bathing, getting her up in the morning, making her breakfast, etc.
What does he say in response?

And what do you tell her when she does that.

What is her father telling her.

I am inclined to guess this is her step dad based on the behavior, with her being so young I wonder how long you have been married to him and how long between relationships, you don't have to answer for me, its not my business just consider it yourself. Children can have a difficult time adjusting to new relationships.

3 year olds most generally try to be pleasing but they are also quite loyal.

1: If she has a relationship with her Dad she may feel that liking your husband is betraying her dad. Kids go through this, they don't want anyone to take their parents' place.

2: If you behave diffrently toward her when he's around she will see him as competition. This just happens sometimes and applies whether it is a parent or step parent.

3: Arguing is natural but she may have heard an argument where you were speaking to him that way and she's mimicking the behavior in that case, modify your behavior and hers will change too.

She just 3 she doesn't know any better... but I'm sure when she grow up more it could get wose or better