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From 1995, a poster showing a flat-tax return proposed by then-Senate Majority Leader Dick Armey and Senator Richard Shelby. CreditDavid Scull/The New York Times 
No matter how many Republicans end up squeezing onto a campaign stage for the 2016 presidential primary debates, one thing is just about certain: Every one of them will vow to cut taxes. So, with as many as 19 contenders all repeating the same message, standing out from the crowd will be a challenge.
For some hopefuls, the flat tax has turned into a way to grab attention.
Ever since Steve Forbes put the idea at the center of his presidential campaign 20 years ago, Republican candidates — and even a Democrat or two — have latched onto the flat tax as a simple and appealing pitch to voters.
So far, at least four Republicans have talked up their support for a flat tax, or a single rate for everyone, which would replace the current system, which taxes richer people at a higher rate on ordinary income than less affluent taxpayers. To lower the rate and simplify the tax code, the flat tax also eliminates most deductions, including those for mortgage interest and charitable contributions.
“I am campaigning on a flat tax that would allow every American to fill out his or her taxes on a postcard that allows us to abolish the I.R.S.,” Senator Ted Cruz of Texas said in April. Senator Rand Paul of Kentucky and Ben Carson, a retired neurosurgeon who joined the race early this month, have also suggested a one-size-fits-all tax, while the former Texas governor Rick Perry pushed a flat-tax proposal during the 2012 presidential campaign.
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Aside from its simplicity, supporters say a flat tax will unleash a torrent of economic activity, particularly if the tax is set at a relatively low rate between 10 percent and 20 percent for individuals and businesses and exempts all investment income, as most of the plans do. But even if economic activity flourished, lowering taxes on the rich means less affluent taxpayers would end up paying more of the overall tax burden.
For all the flat tax’s superficial appeal, that is a difficult proposition to sell beyond a core of true believers.
“It seems like every four years Republicans have this internal contest over who will cut taxes the most, and the conversation is not very deep,” said William G. Gale, co-director at the Urban-Brookings Tax Policy Center, who was a senior economist at the Council of Economic Advisers under President George H. W. Bush. “All these proposals look intriguing to people from a distance, and then they get up close and find out that they don’t like them.”
Mr. Gale said perhaps the biggest flaw in both the flat tax and other Republican proposals to cut top rates from today’s levels was the claim that they would spur a locomotive of economic activity. “It’s ideology,” he said. “The evidence does not support the view.”
Tony Fratto, a Washington consultant who worked in President George W. Bush’s White House, said that talking about a flat tax “certainly in the Republican primaries puts you in safe ground.”
“Yet one of the reasons flat taxes don’t go anywhere in economic circles is that it’s hard to make the math work,” said Mr. Fratto. He has contributed to the campaign of former Florida Gov. Jeb Bush, who favors a different tax-cutting plan.
Even rosy projections about growth and promised spending cuts show that most flat-tax proposals, by setting the rate low enough that it doesn’t look forbidding to ordinary taxpayers, generate too little money to prevent the budget deficit from increasing substantially, undermining another key promise of Republican candidates.
As it turns out, most Americans are also doubters. A survey on tax fairness conducted last year by WalletHub, a consumer finance information and social networking site, found that three out of four respondents preferred a progressive structure over a flat tax. The survey also showed that economic liberals and conservatives both said the fairest system was one in which wealthy households were taxed at a higher rate than lower- and middle-income households — even if they disagreed over just what those rates should be.
Stephen Moore, a senior fellow at the conservative Heritage Foundation, acknowledges that polls show feeble support for the idea.
But he argues that a flat tax can nevertheless be potent because it plays into a strain of deep-seated hostility toward Washington and the Internal Revenue Service.
“The way to sell the flat tax is as the ultimate Washington-versus-America issue,” he wrote in a recent issue of The Weekly Standard, a conservative magazine. “The only people who benefit from a complicated, barnacle-encrusted 70,000-page tax code are tax attorneys, accountants, lobbyists, I.R.S. agents and politicians who use the tax code as a way to buy and sell favors.”
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Mr. Moore, who said he had been advising Mr. Paul on his flat-tax plan, insists “there’s a hunger among conservative Republican voters for something big and bold and simple.” Although Mr. Paul previously talked about a 17 percent flat tax, Mr. Moore said that the current discussions with the candidate were focused on an even lower rate.
For Republicans, championing a flat tax could have a political payoff even if support among the public remains limited. In a crowded and unsettled field, the flat tax enables a candidate to appeal to the party’s most conservative constituents, including libertarians, deficit hawks and Tea Party members during the all-important primary season, even if the plan is abandoned later.
“During the primaries, a lot of people talk about flat,” said Michael R. Strain, an economist at the center-right American Enterprise Institute. “During the general, you won’t hear that, but you’ll hear about a flatter code, with fewer rates than we currently have.”
The federal income tax system has seven tax brackets starting at 10 percent for the lowest earners and climbing to 39.6 percent on upper incomes. There is also a pantry chock-full of exemptions and credits — for child care, home mortgages, retirement savings, among others — while capital gains and dividends enjoy relatively low rates. As a result, few Americans pay more than 25 percent in income taxes and most pay considerably less already.
Senator Marco Rubio of Florida has taken the flatter approach by proposing, with Senator Mike Lee of Utah, a system with just two brackets: one at 15 percent for joint filers earning $150,000 or less; and a second at 35 percent. Everyone would be eligible for a $2,500 per child tax credit.
Mr. Rubio’s plan has ignited enthusiasm among some low-tax activists primarily because it eliminates taxes on capital gains and dividends.
In their view, the flat tax is more of a means to an end: shifting taxes away from income to consumption. When it comes to a flat tax, “most people focus on the rate, which is not that important,” said Ryan Ellis, tax policy director for Americans for Tax Reform, which has been asking candidates to sign a no-new-taxes pledge for 30 years.
What matters much more is the base, Mr. Ellis explained. In his eyes, what is most appealing about flat-tax plans is that they exempt savings from taxes, in theory freeing more money for investment.
One plan, championed by the newest entrant to the race, the former Arkansas Gov. Mike Huckabee during his 2008 presidential bid, would take that concept even further, replacing the entire federal tax system, including payroll taxes, with a national sales tax on all goods and services, whether provided by a doctor or a babysitter.
But like all of the Republican plans for flatter taxes, this idea — labeled the “fair tax” by supporters — has been criticized by economists who argue that the heaviest burden will fall on low- and middle-class families because they spend most of the money they earn on living expenses, whereas investment income is primarily concentrated among the wealthiest Americans.
Mr. Moore expects a “big battle in the primaries” over the economic effects of the plans.
Skeptics raise another question, however: Now that not just Democrats but several Republican candidates are talking about the shaky foundations of the middle class and the widening gap between the rich and everyone else, a plan to slash tax rates that primarily benefits the wealthy may no longer carry the same cachet. Even if it does fit on a postcard.