Earlier quoted context omitted.
Use the Swiss system : when a petition reaches a given threshold of signatures, have a referendum. If the 'yes' wins, it becomes a law. It is easy to add over our current system, it is democratic, it respects all institutions. I don't understand why this idea doesn't have more followers.
I'm very wary of a system like this. It's not working so well in California, for example, where - although its more complicated than this, obviously - the basic end result is that the people keep voting for low taxes, but also more services, and the ring-fencing of parts of the budget.
If you think people will primarily vote for lower taxes, why are you surprised that they would vote for any crackpot who promises to lower them (e.g. Tea Party) ? Representative or direct democracy, if your voting population is made of idiots, you are doomed anyway.