The Republican approach to taxes sounds great on its surface. Cutting the tax rates and making up the difference by ending some tax deductions/credits/loopholes seems like a reasonable, fair way to simplify the tax code. While it sounds great in theory, there can be tremendous shifts in the tax burden with such proposals, depending on the magnitude of the changes to rates and deductions. For an example of a plan which does a poor job of fairly introducing cuts, let's look at the tax plan proposed by Mitt Romney, as well as an analysis (.pdf) of that plan by the Tax Policy Center. By taking the tax debate out of the realm of hand-waving, general discussions which sound good and into actual, specific policy, the deception at the heart of Romney's policy is laid bare.
Romney proposes cutting the tax rate at every income bracket by 20%, dropping the top rate from 35% to 28% and the lowest rate from 10% to 8%. He would make up the lost revenue by getting rid of tax deductions and credits. He has not as yet been specific about which deductions and credits would go, but given where the money is when it comes to deductions/credits, he'd have to end some fairly popular things like the child tax credit, health insurance deductions, or Medicare benefits not counting as income. He had been hoping that he could continue promising the good things without anyone asking about where they come from.
The study by the Tax Policy Center looks at the actual effects of Romney's plan. It accepts Romney's premise that the plan would not result in lower revenues for the government. It assumes that certain tax benefits would be untouchable, such as the capital gains tax rate, which Romney has said he will not raise, or the tax-exempt status of veterans benefits. They then pursue the effects of Romney's proposals on people from different income brackets to test Romney's claim that everyone will still pay a similar share to what they pay now. Their conclusion is that even if every single tax benefit (that's not on the untouchable list) for people making over $200,000 a year, it is mathematically impossible to arrive at a situation where the rich don't get a big cut while taxes go up on people making less than $200,000.
Let's consider a gazillionaire whose tax bill would drop by a few million dollars as a result of the cut of the top rate from 35% to 28%. While things like the child tax credit are significant for an average family, our gazillionaire doesn't give a shit if the credit goes away. The drop from 35% to 28% overwhelms any effects the loss of a measly few credits. According to the TPC, people making $200k to $500k would see a drop in their tax bill of $1,800, and the benefits only go up from there. Meanwhile, for a family of four that actually cares about the child tax credit, their taxes would go up by $2,000.
The authors go on to make every assumption they reasonably can to help Romney's case. They assume economic growth according to models developed by W's chief economist. They assume every tax deduction is entirely eliminated for anyone making $200k+, to squeeze every penny out of them they can before taking away the middle class's benefits.
In response to the study's release, the Romney campaign has responded with ad hominem attacks against the authors and claims that massive economic growth would fix everything. But they don't show their work. They don't say "we think the economy will grow by X%, with Y thousand new jobs a month, so then everyone's taxes change by this much, and that's how it works!" Why wouldn't they release the math behind their claims? Could it be that the math just doesn't exist? The TPC study indicates it's impossible that it ever could.