We only have this on the state level in various degrees. Bavaria has the most experience with easy DD in Germany, and has had good results.
California's direct democracy form (albeit at the state level also) called the initiative system, sounds like it shares some of the conduits of the Swiss system. If you gather enough signatures, you can get a special election, or an initiative on the ballot, or even a "recall" election. (This last one is the way Governor Schwarzenegger was elected, via a mid-term recall of Governor Davis, who was not so corrupt as to be indictable, but was not well-liked, especially by the conservative Republican faction in the State.)
Other states have this process, too, but the result is sometimes very messy -- initiatives are usually poorly or loosely written, and money drives the signature gathering and initiative agenda focus 100%. It's a sharp stick in the hand of the most wealthy individuals and special interest groups. If it's just us, it seems like an awful waste of space. -Carl Sagan, Contact
Anyway, the proposal by Mehr Demokratie is specifically designed for Germany's political system and includes certain safeguards: