This linked Redstate member post gives the details.
By backing the governor into a corner, they have left him no choice but to refuse to stay the course. He could not compromise at this point even if he wanted to do so. More accurately, he could, but if he did so, he might as well resign, because he would get nothing of any substance accomplished for the remainder of his term. Giving in on this now would establish the precedent that he can be coerced into giving in on anything at any time. The next time a controversial proposal came about, the protesters would be twice as loud, and the people on the governor’s side would be hesitant to rally around, lest they be left holding the bag again. Presumably, the governor is no fool and knows this, and so will continue to stand firm.
The unions also seem to have expected public opinion to come to their aid without having good reason to do so. The election itself should have been an indication that the public was no longer on the side of the unions. It’s not that the public is anti-union, per se, but they no longer see unions as representing oppressed workers who are fighting The Man. What they see now is a group that is well-paid and well-perked and yet demands more. At a time of nine-to-ten percent unemployment, with many taking jobs they don’t particularly want because they can find nothing better, most of the public has little use for people who already have good jobs protesting and bemoaning their fate.