I'm not going to deny that the DOE budget (likely) has some waste. That, unfortionately, is a given. And, arguing that Walker needed to do something about Wisconsin's budget problems? Again. That's a given.
The question is how to go about fixing it.
My point was that the linkage between collective bargaining (as a right that the teachers union could retain) was, completely divorced from the state budget in this instance. This was the point that the Union made. Repeatedly.
Walker countered that he needed flexibility to deal with the budget, so collective bargaining had to go. In turn, the Union responded that they would be willing to forgo that right for two years. What did Walker do? He didn't respond. At all. He ducked the issue.
As I said earlier, the Union also agreed in public to all of his cuts. What did he do? Instead, he tried to pivot back to the flexibility point mentioned earlier. Again. Not a way to earn trust. So, the protests were on. It was a display of force on both sides.
Given every opportunity to shape the budget (in a way he wanted), Walker continued to focus on eliminating collective bargaining. So, that more-or-less shows the issue. It wasn't the budget alone as you imply. It was, very possibly, the exploitation of the sitiuation as an excuse to bust the Union.
The bottom line is, Walker could have avoided this entire fiasco if he was willing to preserve collective bargaining. The Union, in turn, wanted to keep that because it was their protection against strong-arm politicans.
So, "what's a governor to do in a state that's hemorrhaging, largely on the back of union cronyism and contracts that have no basis in reality?" A good start would have been to focus on the budget and not try and tack on political "gimmies" to appease your party.