Mitt Romney has two tax principles. First principle: I'm cutting taxes. Second principle: I won't make "people who are at the high end" pay a larger share of total taxes.
About that first principle: Romney wants to extend the 2001/2003 tax cuts cuts permanently and cut each marginal tax rate by a fifth. That would bring the top marginal tax rate, now at 35 percent, down to 28 percent. To make up some lost revenue, he says he'd eliminate some deductions and exemptions.
About that second principle: We don't know who "people who are at the high end" are but we do know that they stand to keep a lot of extra money if Romney cuts federal income tax rates by 20 percent across the board. Remember: About 50% of the country doesn't even pay federal income taxes, and the top 1% pays more overall federal taxes than the bottom 60% combined.
Here's a breakdown, via TPC, of share of income and share of federal taxes (income, payroll, etc). The big blue pizza slice is the bottom 80 percent. As you move clockwise, you go up the income ladder.
You can take a lot of lessons away from these charts including: (a) Yes our tax system is progressive; and (b) yes, the rich pay a lot of taxes, because (c) wow, they sure do capture a lot of the income to begin with. But back to Romney.
Let's assume that Romney's definition of the "high end" is the top five percent. I'll direct your attention to the orange, light blue, and purple pizza slices in the right graph. In order to keep those slices the same shape (which is Romney's second principle) while massively cutting income taxes (Romney's first principle) you have only three choices. You can eliminate a lot of popular deductions among rich people, like mortgage interest. Or you can say, Screw it, we're just going to shrink the size of the pie dramatically and make do with much lower revenue and much higher deficits. Or, somewhat complicatedly, you can have the top 5% pay the same share, concentrate your tax cut on the 80-95% of Americans, and then ask the bottom 79% to pay a higher share. (Or, really, you can see all three things at the same time.)
The upshot is that Romney's simple two-principle approach to tax policy isn't so simple. And no matter what, all conceivable Romney plans violate my own first principle: Don't permanently cut taxes.
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