As of now, we have a system with state taxes ("apples") and federal taxes ("oranges"). Herman Cain's plan is federal tax reform. That means he's taking all the current federal taxes (income, corporate, estate, payroll, etc) and simplifying them to his 9-9-9 plan. It's true that this means you'd be paying 2 sales taxes but that really doesn't mean anything. If I told you that you'd be paying a 5% state sales tax and 5% federal sales tax or a 50% income tax, wouldn't you prefer the double sales tax? The key is not which taxes you're paying, it's the aggregate amount that you'll pay. Unfortunately for politicians, it's not quite as easy to break that down into a soundbite so they instead prey on ignorance and people not paying much attention to what they're really saying. It appears Herman Cain's plan would result in a tax increase for most people but the fact that it results in 2 sales taxes isn't what drives that.
Even if Herman Cain were wrong and they're not apples and oranges, what do people propose that he do about it? States also have income taxes, does that mean his income tax isn't allowed either because there are 2 of them? Should he eliminate the state sales tax with his iron fist? I'm sure that wouldn't bother the states' rights activists at all or cause any federalism issues. A tax is a tax and whether it's the tax you pay at a toll booth on the highway or on a state tax return or federal tax return, it's all money going out and most people really only care about how much money they're actually handing to the government, not the name or type of tax.