I really like the idea, and I wish more countries adopted this. If you're not a big fan of direct democracy and citizen-referendums like in Germany, this one still allows the representatives to have the final say on it. So nothing changes from the republic point of view, but it does offer regular citizens much better access to the Parliament and getting it to vote on laws they care about.
Of course they can still vote no, and they might, but that's why you need to build enough awareness and also try to change the politicians' mind on the issue.
The most recent one was proposed in 2009 and became law in 2010, changing the requirements to run for office (making them somewhat tougher on corruption).
PS: That law was nicknamed "Ficha Limpa". Something like "Clean Slate".