Now obviously there might be some issues ensuring that you get researchers who want to make a real go of trying to disprove it rather than erect straw men and tear them down. But that's probably solvable.
Yes in many respects it would be a big waste of money, but after you poke a million little holes in climate change they will be fixed. And that will strengthen our understanding of the climate and in all likelihood substantially bolster the claim that climate change is real and man-made. And if it takes $100mm or $1b or even $10b worth of very public extra research to really convince people it would be worth it.
The US Global Change Research Program's budget is $2.6b annually so $20mm per year is a joke, $200mm a year is a bit substantial and $2b per year might actually be a reasonable amount.
http://www.climatesciencewatch.org/2012/02/14/presidents-201...
Again I realize that for many people it would be a "waste" of money. But if it was publicized properly (and I do realize that's a big IF) it could go a long way towards garnering the public support necessary to do some economically difficult things. When politicians are happy to kick the can down the road every couple of years it's pretty tough for the public to understand why this is an issue that can't be kicked as well.
EDIT: I also realize it's stupid to waste taxpayer money, something I'm vhemently against. But while I'm dreaming here, let's suppose that the money is taken from the military budget for the duration of the grant period.