As far as the immediate short-term is concerned, union-busting has not been good for the popularity of Republican governors. According to the most recent polling, Wisconsin's Scott Walker has an approval rating of 43 percent, while Ohio's John Kasich has tanked with an approval rating of 35 percent. Neither governor enjoys majority (or even plurality) support from independents, and both rely on heavy Republican support to buoy their approval ratings.
For now, this is good news for Democrats. In the long-term, however, I'm not so sure; on the whole, job approval has more to do with economic performance than it does with good policy or political strength. In all likelihood, if the economy improves, it won't take much for Kasich and Walker to claim credit and restore their standing with voters. By contrast, state Democrats will benefit if the economy stays weak and union-busting remains a salient issue.
It's worth noting that we're basically witnessing a reverse of the last two years in Washington; Democrats form the intense minority, and Republicans are trying to use their large electoral advantage to pass ambitious legislation. Indeed, the parallel extends further: as with Republicans and health care reform, Wisconsin Democrats are planning to challenge the legality of Walker's union-busting.