Often, it takes fewer than that. They don't have to be geniuses or wealthy. They simply have to be committed to seeing their goals through.
It's enough people to form the board and lead volunteers of a powerful non-profit group. Any Occupy group with that many active leaders is staying strong.
Most Presidential primary campaigns can be run with twelve staff until the race goes national. It's more than enough key volunteers to run a serious campaign for other elected offices like State Representative or Mayor.
Even Jesus started out by recruiting twelve apostles and look how that turned out.
It's a small number but most groups have trouble finding that many dedicated people. It's not hard to get someone who will help out once in a while. Finding twelve people who will really spend their time, energy, and passion toward a common goal is difficult. Most groups accomplish a great deal with 6-10 leaders, but still never reach that world-changing threshold of twelve hard workers.
Our educational and political systems usually emphasize individual action and the power of individual leaders, instead of the power of movements. Long work hours and family obligations are barriers for most. And you can always play a pretend life on the computer instead of living a real one for yourself.
But, if you can manage to find at least twelve people motivated to work hard together on a project, I'm absolutely certain that big things will happen. I've seen it done. That's all it really takes.