In reality it is actualy a really tough slog building up the number of signatures on a petition. You need good social media contacts and you have to work hard to get your petition noticed. If it is highlighted in a newspaper article it might take off and gain a lot of signitures very rapidly, but that is the main issue just getting noticed.
I called 38 Degrees earlier today to find out what was going on with this petition; they will be getting back to me on it.