There are some huge complications here.
In some sense the US is one of the poorest nations in existence. Name any other nation with a debt anywhere close to 10.8 Trillion, and an out of control deficit?
Also in the US there are some incredibly wealthy people who are doing the right thing, look at Gates, Clinton, and various other "retired" individuals who run charitable foundations that are investing in projects to make a huge difference.
With all due respect to MMI, people have been throwing money on the problem for an entire generation, and if money were all it took to solve the problem it would be done by now. All the research in this area points to it being far more complicated than that.
At an individual level I think its a matter of individual rights and beliefs. I personally am not that well off and I sometimes give to causes I believe in, but claiming someone has a duty to throw money on a non-solution to a problem is rather extreme.
I think if you needed sizable donations from the rich for a plan to remedy global poverty you'd see a lot of success, provided the plan was going to work and could convince people it was going to work. Lots of people are jaded to Project X, Project Y or Project Z that will "save Africa" because their previous donations resulted in no real change, and those projects have largely failed spectacularly.