Guys and girls,
Who gives a toss what the public think. I (and 146 others) went through all this last year at Ansett NZ (now Qantas NZ). It's not a slinging match between you and the public; it's between you and the company. Having said that, it would be bloody great to have the public on your side.
The company WILL resort to dirty tactics - be prepared for it (it sounds like they have started already). Hold your ground and do whatever you have to, to maintain your conditions. Don't let any scabs or management get you down.
Good luck.