I don't know about that... In Labor economics 320 at the University of Michigan, we learned that unions also push for increases in the minimum wage laws - even though almost all union workers earn well-over the minimum wage - because of the ripple effect that increases in the minimum wage have for all hourly wage workers. So even though only 1.6MM workers earn min wage, and 2MM earn below min wage (representing approx 5% of all hourly wage workers in the U.S. according to the stats in the study I linked to in my other post), an increase in the minimum wage would benefit all workers. Seems like if the minimum wage increase were really that ineffective, or alternatively bad for workers (you seem to be arguing both), you wouldn't have big business all uniformly opposed to it.
Also, in the same class, as well as other upper-level economics courses, we learned that companies that can exercise market power (e.g. every large multi-national or multi-state corporation in the U.S.) are not subject to the usual supply/demand competitive pressures of the market. And, counter intuitively to the basic supply/demand graphs one learns in Econ 101, controls like price ceilings, minimum wage laws, etc. have the opposite effect on such employers, compelling them to produce more goods at lower cost or hire more workers, respectively.
as far as a bump in the minimum wage costing jobs, I suppose you could conceivably imagine some small mom-and-pop grocery store that hasn't already been Walmarted out of business, operating on razor thin margins, that if they were forced to pay their 16-year-old grocery baggers more than $7.25 hour, would have to simply lay some people off, and force the others to work more hours or work faster. seems like a stretch... any small business that unprofitable would probably close up shop anyway, but they may exist.