Stop.
No. IT IS NOT a responsibility. Why is it just billionaires? If you had said 'everyone', I would have given you a wider berth, but here you are. Responsibility equates with obligation, obligation equates with duty. So therefore, you are obligating them to give.
"It's amazing to me how many people think that voting to have the government give poor people money is compassion. Helping poor and suffering people yourself is compassion. Voting for our government to use guns to give money to help poor people is immoral self-righteous bullying laziness. People need to be fed, medicated, educated, clothed and sheltered. If we're compassionate, we'll help them, but you get no moral credit for forcing other people to do what you think is right. There is great joy in helping people, but no joy in doing it at gunpoint."
-Penn Jillette