Your comment, about looking at the minimum wage increase "from both sides", reminds me of a comment about oats...looking at oats from the front end of a horse, and then when the oats come out the "other side".
As I've had fairly extensive conversations with some business owners who employ almost exclusively minimum wage workers, what I've learned is that the only cuts they absolutely have to make from increasing worker's wages are minor cuts to the very comfy lifestyle they have.
Any business that can't afford to pay for "necessary" items because of an increase in the minimum wage isn't being well managed. The type of "reason" you cite is always the first used by exploitive business owners or managers, and seems to never be borne out in practice.