Helping someone who doesn't want to help themself

I have a situation right now with a family member where they need some help. I visited with them and felt compelled to help them. The reality is that I have three kids, two part time jobs and a house to run. I offered what I thought I could and come to find out they haven't done anything for themselves to make things better. When I offered to help I thought I knew the whole story but I found out later that I didn't. I'm not willing to step in and do everything but I do want to help because I think that's what God wants from us as his followers. I'm disappointed though that they are willing to step out and do something to help with their situation. I know I'm being vague, but what do you do when you see a need, try to meet it and then find out they really want you to do everything for them and they don't want to step up and take care of things on their own?