Perhaps they wouldn't want to lose out on the revenue but since this amount of money would get a good deal of press maybe Google would consider doing the ads at a discount or pro bono. It seems like the kind of thing Google would be in to. If and when the Facebook group gets decently big (25k?) we could inquire about that possibility.

50,000 users would surely count as a critical mass, meaning that each member of the Facebook page effectively created $20,000 for charity.

This also means that each new member you recruit is like creating $20k for charity. Worth mentioning that on the Facebook page.

Recruiting support for causes is usually a lot easier if you can say in concrete terms what the cause will accomplish. Maybe 1 billion is a big enough number that it doesn't matter but I suspect being able to say things like "Will feed 100,000 children" or "Cure disease x" helps charities get support.

Maybe we could some of the copy could say things like: "If 1 Million Dollars will feed 100,000 starving children... imagine what 1 billion dollars could do." Better yet if they are things that have actually been accomplished. So "If $23 Million a year erradicated smallpox, imagine what $200 Million a year could do." Etc. You could do 3-4 of these. That way you give a sense of the kinds of things that their participation could lead to without having to know exactly how the money will be spent.

Also, since it is starting with a facebook page, make sure to check out Facebook's advertising options if you haven't yet.

Edit: Is there any particular way I can help you with this. I'm a broke college student so I can give a little money for ads but if there is anyway you can use my time, I'm in.