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The Republican Party is catching flat-tax fever, setting up an election-year fight with Democrats over whether wealthier Americans should pay more taxes or get tax cuts.

Republican presidential candidate Mitt Romney became the latest to punch the tax button Wednesday, telling a Virginia audience that he'll soon update his economic proposal to spell out how to flatten the tax code.

A day earlier, rival Rick Perry proposed an optional flat 20 percent tax on income. Both followed Herman Cain's pitch for a flat 9 percent income tax as part of his 9-9-9 plan, which helped him jump to the top tier of candidates for their party's 2012 nomination. Newt Gingrich and Michele Bachmann also support a flat tax.

A flat tax -- so called because it would set one tax rate for all income groups while taking away many or all deductions -- would simplify taxes. It also would almost certainly give big tax cuts to wealthy Americans. Republicans say cutting taxes, especially on the wealthy, helps spur investment, economic growth and hiring.

At the same time, most of the Republican candidates propose other changes that also would mean big tax cuts for high-income Americans, such as eliminating taxes on dividend income or capital gains, and eliminating the estate tax, which Republicans call the "death tax."

Their push comes at the same time that President Obama is pushing to raise taxes on higher-income Americans. He has proposed raising taxes on those making more than $200,000 and has endorsed a push by Senate Democrats to raise taxes on incomes above $1 million.

The debate comes as new data show that the wealthiest Americans have greatly increased their share of U.S. income in recent decades. The richest 1 percent had 17 percent of U.S. income in 2007, more than double their 8 percent share in 1979, according to a report this week from the non-partisan Congressional Budget Office.

A flat tax on income would take away some deductions but lower the rate. Perry, for example, would cut it to 20 percent. Gingrich would cut it to 15 percent. The wealthiest Americans now pay a 35 percent marginal rate on income above $379,950. A detailed analysis by the Tax Policy Center found that the Cain plan would mean an average tax cut of $455,000 for those with incomes above $1 million.

In 1996, Romney criticized a flat tax proposal as a boon to the rich, going so far as taking out newspaper ads in early primary states to criticize the proposal from Steve Forbes, a Republican presidential candidate.

"It's a tax cut for fat cats," Romney said then.

When he announced his economic agenda this year, Romney said he would pursue a "long-term goal" of a "flatter, fairer, simpler structure." But he also said he wouldn't change any of the existing personal income tax rates.

While the Republican tax proposals would give tax cuts to the wealthy, the candidates have backed away from the appearance of raising taxes on lower-income Americans.

Cain at first denied that his plan would raise taxes on poorer Americans, then changed it after the Tax Policy Center found that the 84 percent of taxpayers would pay more under Cain's plan.

Gingrich notably would keep the earned income tax credit, which helps lower-income families offset payroll taxes for Medicare and Social Security. "Preserving the EITC and child tax credit are critical to ensure that the optional flat tax system does not unfairly target low-income Americans," Gingrich said.

Perry would give all taxpayers the option of sticking with the current tax system, meaning that no one would have to pay more than they would under today's rules.

"That is the wise political move," said Grover Norquist, president of Americans for Tax Reform, which supports tax cuts. "He doesn't say to low-income people, 'We're going to come to get you.'"