Here is the key point about the first limit of libertarianism, which libertarians have a hard time grasping. This is the argument:

Since the Good Samaritan has no right to pass by and leave the unfortunate person to bleed to death, and since you have no right to pull your shoulder away when someone touches it to regain his balance (so that he doesn't plummet to his death), libertarianism is therefore false. The duty the rich have to the poor is analogous to those cases. The rich have no right to let the poor in America die of starvation or exposure.