Don't get me wrong. Granholm, a Democrat in a state where organized labor remains powerful, is a big proponent of a higher minimum wage. It's just that she would have rather raised the minimum wage through a constitutional amendment on the ballot this fall than through legislation. That could have had the convenient side effect of bringing lots of Democratic union voters to the polls to also vote for her reelection. Once the statutory increase became inevitable, however, the groups pushing the constitutional amendment called off their effort.
This, of course, was exactly what the Republicans who control the legislature intended when they supported the bill.
Many of them had previously opposed minimum wage increases and openly said they didn't like the legislation. But they also said they were concerned about a large Democratic turnout in November (besides hating the idea of putting the minimum wage in the constitution) and hence supported the bill.
This type of maneuvering certainly isn't unique to Michigan. Stateline.org had a good summary of referendums recently and it's not hard to see how some of the most widespread ideas could be intended to alter election results, just as much as they're intended to alter public policy. While minimum wage increases on the ballot could bring Democrats to the polls, gay marriage bans and new eminent domain restrictions are likely to draw Republicans. I don't think it's too cynical to say that while some proponents of these measures earnestly believe in them, others are more concerned with their effect on turnout.
It's an open question, however, whether these initiatives really can have a big enough effect on who shows up to make much of a difference. Certainly the possibility of them having an impact seems more plausible in a midterm year such as this one, as opposed to a presidential year, where almost anyone who cares about politics votes anyway.