This sounds logical until you realize that there are petitions with very large numbers of signatures (relative to petitions more broadly), that we also have pol

This sounds logical until you realize that there are petitions with very large numbers of signatures (relative to petitions more broadly), that we also have polling for and that are, from polling, relatively unpopular. If the people who care care a lot, then you can get a sizeable petition (again, relative to petitions generally) even if there aren't a ton of "lurkers" who also support it but aren't signing. And this pattern of "small but very passionate minority vs large and slightly anti- majority" is a relatively common one (or flip the valences). There is probably a correlation between number of signatures and broader appeal, but I would bet that it's a very weak one.