In the Swiss system a federal referendum must be initiated if 50,000 people or 8 Cantons have petitioned to do so within 100 days.
Referendums within Cantons don't need so many people and may be triggered by other rules. For example if expenditure exceeds certain levels.
Referendums on changes to the constitution, or joining international organisations for trade or defence, require 100,000 signatures within 18 months.
In the past, the government has often initiated counter proposals that have won out. Reports suggest that even the threat of a citizens initiative has prompted the Swiss Parliament to reform the law without the need for a referendum.
More from wikipedia here.
The proposed Interactive Democracy system could easily be modified to accommodate an ePetition with a certain trigger level, say 50,000 people. On the other hand, a system that allows the most popular petition to rise to the top of the list and be considered by Parliament, may have the effect of integrating those people interested in politics into the system. In particular, members of political parties would be likely to contribute their signatures and, therefore, have more say over Parliamentary business and the conduct of their Party.
Having a long list of ePetitions, some of which may be quite radical, may foster debate and initiate better, more creative proposals that rise to the top. All of which is much easier to do with an Internet based system. It will be interesting to see how Swiss Direct Democracy adapts to the web.