The proposal by Mr. Perry, the Texas governor, does not yet have details, but it is expected to resemble a version previously advocated by the former presidential candidate Steve Forbes, who has advised Mr. Perry on his plan. Mr. Forbes’s proposal in the late 1990s featured a 17 percent tax rate.

Mr. Romney has previously been critical of a flat-tax system, including in newspaper advertisements he took out in 1996 as a “concerned citizen” in which he argued that the Forbes tax plan was  a “tax cut for fat cats.”

Lately Mr. Romney, the former Massachusetts governor, has been more nuanced, arguing at a town hall meeting that he was concerned that too flat a tax structure would hurt middle class taxpayers and emphasizing that while there are some good attributes to a flat-tax system, he prefers tax breaks for the middle class.

Other candidates have also taken up the mantle for simplifying the tax system and broadening the tax base.

Herman Cain, a businessman from Atlanta, had entered the race as a relative unknown but has vaulted to prominence partly because of his plan resembling a flat tax (plus a national sales tax). Mr. Perry appears to be trying to harness the popular tax frustration that Mr. Cain has tapped into, and simultaneously differentiate himself from Mr. Romney.

A major result of adopting a flat tax would generally make the tax system more regressive, thereby reducing the percentage for high-income earners but increasing burden on lower-income groups.

“It’s just simple basic math,” said Chuck Marr, director of federal tax policy at the Center on Budget and Policy Priorities, a liberal research group. “To the extent that it is revenue neutral, a flat tax implies large tax increases on middle-class people and, mirroring that, a major tax cut on wealthy people.”

For some conservatives, however, the regressive nature is actually a positive result of the flat tax system. Under current policy, the wealthiest earners are paying a higher tax rate than the poorest, with some Americans paying very little or no taxes.

That fact has angered many Americans who think they are shouldering too much of the country’s tax burden. The “99 Percent” slogan of Occupy Wall Street protests, for example, has been countered with a “53 Percent” movement, referring to the fact that 53 percent of Americans pay federal income taxes (although many more pay payroll taxes).

The effects of these various proposals aside, replacing today’s labyrinthine tax system with a flat tax does have the virtue of simplicity. Americans would spend less time, and endure fewer headaches, figuring out how much they owe the government.

“Simplicity is good, but that’s not all you want,” said Roberton Williams, a senior fellow at the Tax Policy Center. “If all you want is simplicity, you could just tax everybody $10,000. That would be easy and simple. But most people wouldn’t think that’s fair.”

A flat tax would be a major ideological victory for many economic conservatives, akin to how some social conservatives feel about overturning Roe v. Wade. Besides Mr. Forbes’s plan, several other Republican leaders like Phil Gramm (also now advising Mr. Perry, according to Mr. Forbes) and Dick Armey have proposed their own versions over the years but with little traction.

Grover Norquist, the founder of Americans for Tax Reform, an influential conservative group, said all the candidates were moving toward a flatter tax structure. “Now it’s a consensus position in the center-right,” he said, compared with 15 years ago, when Mr. Forbes’s plan was attacked by other Republican candidates.

The presidential candidates advocating some version of a flat tax, however, denied that their proposals were regressive.

Adam Nagourney contributed reporting.

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