While yes, I believe you are ultimately correct,
  that way of thinking, "It's not going to happen" combined with
  "Therefore I am justified in doing nothing", will become a
  self-fulfilling prophecy.

  I have a different excuse for not signing the petition that can
  lead to a proposed amendment; I really don't care either way.

  If someone said, "KEN PLEASE PLEASE SIGN THE PETITION IT WOULD
  MEAN _SO MUCH TO ME_" then, if it's somebody that was important
  to me, I'd sign it.

  But otherwise, I genuinely don't care either way.

  I don't care if it's successful, if it fails, if it generates
  political fire or dies; I really don't care.

  I'm using your words as an example; not picking on you in
  particular. I mean there's many OTHER logical reasons not to
  care as well: percentage of conservative vs liberal voters
  blocks in Florida, Florida's need to get away from the "image"
  of beng drug-trafficking capital of the USA, an image they've
  been TRYING to shed as a state for decades., and even the
  failing of recent medical marijuana - which died in
  committee[1]http://ballotpedia.org/Florida_Medical_Marijuana...
  - are all seemingly valid justificatoins for voter apathy.

  Nevertheless, they're still ridiculous reasons.

  The GUARANTEED way to keep something from happening is doing
  nothing.

  The rest are just "maybes". It's the apathy that bugs me, even
  though its not my issue. You'd think it was by my passion here,
  but my passion is for complainers complaining, seeing a virtual
  piece of paper that just have to stick their name on and going,
  "eh, I have to click and type my name. No point in doing that
  because: [insert elaborate justification here]." - that's what
  my passion is about, whatever the issue is; even if it was one I
  disagreed with.

  I believe in the process, when carried out, or at least the
  attempt. The success or failure of the final result is often out
  of people's hands, but given enough repetition of effort over a
  span of many voting seasons, changes can eventually happen.

References

  Visible links
  1. http://ballotpedia.org/Florida_Medical_Marijuana_Amendment_(2012)