Unions are one of the only major sources of funding for the Democratic party. If Republicans can weaken that, they can strengthen their own party tremendously. No money = no campaigning = no democrats in office.
Politicians don't care one bit about people, they care about their power. This is simply a stab at the jugular of the Wisconsin Democratic party; an attack on the 'enemies' primary money source. Hence the huge counter-reaction of walking out to prevent it. It's an internal power struggle... neither side cares about how it affects the people.
The exact same thing can be said about unions themselves. One of the big union bosses is out on the stump already. Union leadership couldn't care any less about the people.