But that assumes lower-income families won't substitute something else, or just stop buying soda...If lower-income families are drinking a lot of soda, it's only because it's disproportionately cheap compared with healthier foods and drinks.I really doubt that last statement's true since water's far cheaper and healthier than soda.
People buy soda for the same reason they buy anything else: it's the best value given the price. Yes, I'm sure if you increase the price people will buy less of it but they will shift to options that, when you consider costs and benefits, are less desirable. Even if they end up spending the same amount of money on groceries they are worse off than before the tax, by definition. They can only be made equally happy if they spend more.
This point deserves stress. The standard cannot be "if people are spending the same amount as before, then they are largely unaffected." That's a nonsense comparison. You must weigh the costs (including not just money but time, risk, etc) and the total benefits. Or, if you can, hold everything else equal.