Have any of these petitions actually resulted in significant policy changes? Seems to me that the system is just a way to pacify would-be protesters by giving them an outlet for their discontent that has a low barrier to entry.
Also, I have heard that Congress has a rule of thumb - if more than three of their constituents take the time to write and mail an actual letter about the same topic, and they're not looney's but serious-minded people, that signals it's a real issue amongst their constituents and something that needs to be on their radar.
I suspect this petition system works similarly.
That's right, only the important petitions get that many signatures:
https://petitions.whitehouse.gov/petition/deport-justin-bieb...
[currently at 233,220]
Uploaded a couple of days ago: http://youtu.be/ybXKBJ0xDNU?t=10m35s