An honest no hurts less

If you promise someone that you will do something and then you don't you make things worse for them. An honest no would have kept them searching for help. Since you said you would do it they quit looking for help and that could do unnecessary damage to them with far more consequences than the fact that your word means nothing. If you don't want to help or if you can't help then just simply say no sorry I can't help you. Saying yes when you have no intention to help is like throwing someone a life preserver but pulling away before they grab it only for your boat waves to drown them.