Very sorry to hear this, as we suffered the same, for years.
#1 - How do you know what the mother is saying to the child?
#2 - If a mother is so bent on alienating a child from his father that she tells the child things as extreme as "Daddy's abusing you," things may very well escalate as the child grows older. If Mom feels threatened by the child's bond with the other parent and wants to dominate and control things even when the child is so little, she may feel even more threatened as the child goes to school and branches out into other relationships. It may be important to her to feel she dominates and controls those relationships, too - and to try to guarantee that all new people in the child's life (teachers, friends' parents, soccer coach...) see her as the "good" parent and your husband as the "bad" one. So if you can't prove what she's doing to the child now, if it continues, in the future there may be more concrete examples of her effort at alienation and adults who could be called to testify about it, if needed.
#3 - You might consider a custodial evaluation. You'd want a private (translate: costly) one, so the person really has time to ponder your situation. (Here, there are public service agencies which perform them under court order, but they're swamped and therefore I wouldn't rely on them to recognize or have time to deal with subtleties.) An evaulator might be able to recognize:
* A disconnect between the child saying Daddy's abusive and her not being able to give any actual examples of abuse. That's a hallmark of a kid who's just parroting negative talk.
* The mother's negative attitude toward the father.
* That the child seems more comfortable and affectionate with the father when she's alone with him, but then speaks ill of him when she's with the mother - which suggests who's manipulating whom.
If there's not enough evidence at this point to convince a court to change custody, the evaulator probably won't recommend that - but he/she might very well recommend giving your husband more visitation, to offset the negative messages the child gets about him from the mother. And such a recommendation would definitely be helpful background evidence, if things escalate in the future and you DO fight for custody.
#4 - You might also experiment with communicating with the ex through e-mail, so there's a written record. Your husband could raise the issue with her - not in an accusatory way, but one good parent to another, discussing a concern about their child: "Our daughter is saying disturbing things like 'abuse'. I can't fathom where she'd pick up such ideas - or such terms - at age 3. If you do understand this, could you enlighten me? Has she been exposed to some age-inappropriate things on TV or at daycare? What do you think is going on?" If Mom is so bitter toward your husband, she may write him back and vent about all the things she thinks he does which are abusive and her belief that the child shouldn't/doesn't want to be around him. That would be a concrete indication of the thinking that influences the child, at her house, which you could take to a custodial evaluator or possibly to court. Keep in mind: there's no need to respond to such vitriol, point-by-point (although it's tempting). He should only say, "Of course I don't abuse our daughter and it's shocking and upsetting to me to know that you think such things and evidently send this message to our child." After that, it should be handled with objective, third-party help.