Really though? My intution is that democratic governments are very sensitive to issues that lots of people care about, particularly if they show that they care about them by paying real money.

For comparison, the National Rifle Association has 5 million members, and a revenue of $256 million (so ~$50 per member), and is considered to have a big influence in politics. Google's online petition against the Stop Online Piracy Act (SOPA) gathered 7 million signatures ($0 per signer), and the act failed. This "build your own powerplant" movement would be similarly sized.