1) I don't think poverty can ever be "eliminated". Primarily because, to some degree, it's a relative measure. For example, if we say below $20K/yr is poverty, when everybody reaches $20K/yr the new threshold will be $40K/yr. There will always be people who do better than other people, and not necessarily through any fault of their own.
2) Piggy-backing on #1, for some people it will be through fault of their own. They simply don't want to put forth the effort to do better. They're satisfied with what they have.
3) For the most part rising above poverty is an individual task. Leave people alone and let them do it. Government *can* help, but only in a limited sense, and certainly not to the degree of alleged help we see our government(s) doing now.