https://petitions.whitehouse.gov/responses/more/all/12/2/0
Here are a few more I've found poking around:
[1] https://petitions.whitehouse.gov/responses/more/all/1/3/3 [2] https://petitions.whitehouse.gov/responses/more/all/1/3/4
Maybe there's a documented API somewhere, but the queries seem to follow a pattern ala:
https://petitions.whitehouse.gov/responses/more/all/[$pageID...