Jeb Bush and other Republican presidential candidates have recently introduced a lofty goal into their campaign platforms: 4 percent growth in the country’s economy — or, in some cases, even more.

Most economists agree the number is arbitrary and implausible; many have called it downright impossible. Now, Bush and others face the daunting prospect of explaining their math, much of which hinges on policy proposals that, at this early stage, are sketchy at best.

Bush tripped up for the first time last week when he said the 4 percent objective would demand that Americans “be a lot more productive.”

“Workforce participation has to rise from its all-time modern lows,” Bush said during a meeting with the New Hampshire Union-Leader editorial board. “Means that people need to work longer hours and through their productivity gain more income for their families.”

Democrats immediately seized on the remark. In a major speech on the economy this week, Hillary Clinton said Bush “must not have met very many American workers.”

“Let him tell that to the nurse who stands on her feet all day or the teacher who is in that classroom, or the trucker who drives all night,” Clinton said. “Let him tell that to the fast-food workers marching in the streets for better pay. They don’t need a lecture. They need a raise.”

Bush explained later that he was referring to workers whose hours have been cut, and the Union-Leader backed up his logic. “Bush was exactly right,” the paper’s editorial board wrote.

But the incident illustrated the policy contortions that will be required of candidates pushing for 4 percent GDP growth or higher.

Pivotal to Bush’s argument is his record in Florida, where the state’s economy grew at 4.4 percent while he was governor. But that pace likely owed much to the housing bubble, which collapsed on itself in 2008 after Bush left office.

“There is not a reason in the world why we cannot grow at a rate of 4 percent a year,” Bush said last month when he announced his candidacy. “And that will be my goal as president.”

Other Republicans have echoed Bush’s economic optimism, many of them latching on to the same number, 4 percent — a pleasantly rounded, big-sounding number.

In May, Chris Christie unveiled his “Five-Point Plan to take America to 4 percent growth.”

In March, Ted Cruz told Fox News: “If we can get back to historic levels of growth — 3, 4, 5 percent — suddenly, the federal budget picture transforms.”

Scott Walker followed suit last month. “I think we could go from the stagnant growth we have today anywhere to upwards to 4.5 percent if with did dramatic growth, pro-growth policies that are not just about reining in taxes,” Walker told Fox News.

In economic terms, such a growth objective is rather shock-and-awe. Since the economy began to rebound in 2009, growth has averaged just 2.2 percent.

“Let’s face it, 4 percent sustained economic growth would be out of range of what we have had for most of American economic history,” said Allen Sinai, co-founder of Decision Economics, where he is CEO and chief global economist.

But if the threshold is something of a pipe dream in reality, it has often been paid lip service in presidential politics by candidates who recognize the persuasive power of a positive economic message.

During the 2011 presidential election, Minnesota Gov. Tim Pawlenty reached for an even higher number than Bush: “Let’s grow the economy by 5 percent, instead of an anemic 2 percent,” he wrote in a Chicago Tribune op-ed.

“It's been done before,” Pawlenty noted. “Between 1983 and 1987, the Reagan recovery grew at 4.9 percent annually. Between 1996 and 1999, under President Bill Clinton and a Republican Congress, the economy grew at around 4.7 percent annually.

That benchmark is not solely the creation of Republican candidates. The Democratic Party and its candidate, John F. Kennedy, used the same number to rally voters during the 1960 presidential election.

“We Democrats believe that our economy can and must grow at an average rate of 5 percent annually,” the party platform read that year — setting a goal of nearly double the average growth rate from the preceding seven years.

A 5 percent marker, and even 4 percent, has always been ambitious. But many economists argue that it is even more so now in a changed economic landscape.

The nonpartisan Congressional Budget Office has projected that the economic growth will average 3 percent in 2015 and 2016, with a dip in 2017 to 2.5 percent. Later, the outlook dims: Between 2020 and 2025, the CBO estimates GDP growth at 2.2 percent, with labor growth stifled as baby boomers retire.

Economists who argue sustained growth at 4 percent is possible have pointed to Reagan’s presidency, when the economy grew at nearly 5 percent. But women at that time were entering the workforce in historically large numbers, expanding the country’s productivity.

Underpinning the political argument for 4 percent GDP growth is not just optimism alone, however, but a push for substantial changes to tax policy, welfare, trade and spending, among other areas.

In the Wall Street Journal recently, Kevin Marsh and Glenn Hubbard, an economist who has advised Jeb Bush, wrote that “setting a goal of 4 percent growth invites meaningful policy contributions from those who would be our leaders.”

“Many leading economic thinkers judge the economy’s underperformance as unrelated to the policies adopted in the last several years. Instead, their thinking goes, the economy is no longer capable of performing as in previous recoveries,” Hubbard and Marsh wrote. “... We strongly disagree. A more vigorous recovery from the financial crisis was an opportunity squandered. Even today, the economy can grow at significantly higher rates than the prevailing pessimism.”

But there is profound disagreement even over the magnitude to which policy changes can grow the economy.

Last month, the International Monetary Fund presented findings that reforming spending and revenue policies could grow advanced economies by ¾ of a percent. But Doug Elmendorf, a former director of the CBO and incoming dean of Harvard’s Kennedy School of Government, cautioned in a response to the IMF’s paper that such effects are often exaggerated.

“Economists should be careful not to overstate the potency of positive policy changes, because subsequent disappointments can undermine people’s confidence in economic analysis,” Elmendorf said.

To hedge expectations, perhaps, Republicans have so far sought to present the 4 percent growth marker less as a promise than as something to aspire to. But aiming for such nuance can be politically risky.

“If a candidate says, ‘I’d like to see 4 percent growth,’ it’s going to be seen as a campaign promise,” said one Republican who has advised presidential candidates on policy.

And each candidate will need to back up his promise with concrete proposals, which will be subject to the full scrutiny of the electorate.

Some economists have practically dared them.

Gene Sperling, the diminutive former head of the National Economic Council under President Obama, recently told the New York Times: “My personal goal is to be six feet tall and have a six-pack stomach, but I don’t think most people would think either Gov. Bush or myself have a very viable plan for reaching our targets.”