The way I see it, the rich have a responsibility towards the poor, but the poor do not have rights.
It might seem contradictory at first read, but there is a subtle difference. If the rich have a responsibility to help the poor, but the poor don't have rights, that means that the rich have the responsibility to help the poor to the degree that their resources will allow; but the poor will have to make do with those resources.
If the poor have the right to a minimum of resources, then the state must borrow to make up the difference, and that cannot be sustained over time. If the rich have obligations but the poor have no rights, then that forces the state to help the poor in the best manner possible with the resources at hand, which may require tough love policies on occasion.
With rights come responsibility... There's no 2 ways about it and it isn't dependent on income