NEW YORK (CNN/Money) - Alan Greenspan told Congress last week that a slowdown in productivity was probably the key to stronger job growth this year, and he seemed optimistic it would happen, and fairly soon -- echoing a similar recent promise by the White House.

But some of Greenspan's colleagues at the Fed seem to doubt the fall-off in productivity will be significant, and many other economists share their doubt. If they're right, then the labor market's pain could be longer-lasting than Greenspan and President Bush expect.

Productivity, a measure of how much workers produce per hour, has grown at a blistering pace in recent years, as businesses have invested in new technology and otherwise learned to operate more efficiently.

While productivity typically leads to job growth and higher living standards in the long run, in the short term it has helped to make the current labor market the most anemic since the Great Depression.

"New hires and recalls from layoffs... are far below what historical experience indicates," Greenspan said in his testimony. "To a surprising degree, firms seem to be able to continue identifying and implementing new efficiencies in their production processes and thus have found it possible so far to meet increasing orders without stepping up hiring."

The 12-month percentage change in the nation's payrolls has been down or flat for 31 straight months, the longest such stretch since the Labor Department began tracking the data in 1939.

But the White House, in its semi-annual economic forecast, predicts all that will change this year. The administration expects productivity growth to slow from last year's annualized 4.2 percent pace to just 1.5 this year.

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The relationship isn't perfect, but a common rule of thumb for forecasting job growth is to subtract the rate of productivity from the rate of economic growth. Assuming economic growth this year of 4.5 percent -- roughly the consensus forecast of many economists -- and productivity growth of 1.5 percent, you get payroll growth of 3 percent.

"That is about average for a recovery," Gregory Mankiw, Chairman of the President's Council of Economic Advisers, told Congress last week. "It's above the recovery we saw in the early '90s, but significantly below the recovery we saw in the early '80s. So it's a very sort of plausible forecast."

But 3 percent job growth would create roughly 3.8 million or more jobs this year, or about 320,000 a month, and very few economists -- if any -- have a similar forecast. That's mainly because few, if any, expect productivity to slow enough to generate that many jobs.

"We're not going to get the 1.5 percent productivity growth necessary to produce all those jobs," said Anthony Chan, chief economist at Banc One Investment Advisors. "Such a fall-off would be out of line with what normally happens."

Chan has studied productivity in previous recessions and recoveries and found that productivity growth is often fast in the first two years of a recovery and then slows in the third year.

Chan estimates productivity growth will slow to about 2.7 percent this year -- the third year since the 2001 recession -- which would result in job growth of about 150,000 jobs a month, or 1.7 million new jobs for the year.

In order for the White House job forecast to come true at 2.7 productivity growth, the economy would need to grow 5.7 percent this year or faster, which would be the highest annual growth since 1984, and is far higher than any economists are forecasting.

"It's difficult to foresee a growth rate where we will find 320,000 jobs" each month, Chan said.

Of course, productivity hasn't behaved in this business cycle the way it usually does. Instead of slowing as it has in past recessions, productivity continued to grow during the 2001 recession, and 2002-03 was the strongest two-year span for productivity since World War II.

Greenspan and some other economists believe businesses have spent the past few years recovering from the hangover of the late-1990s tech boom, shedding a bunch of unnecessary workers and finally learning to get the most out of all the machinery purchased in the run-up to Y2K.

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According to this view, recent strong gains in productivity have likely been a one-time phenomenon. But some of Greenspan's fellow policy-makers aren't so sure.

"Prospects for sustained high rates of increase in productivity are quite favorable," Fed policy-makers wrote in their semi-annual policy report to Congress. "Businesses are likely to retain their focus on controlling costs and boosting efficiency by making organizational improvements and exploiting investments in new equipment."

They didn't offer any firm predictions about productivity growth in 2004, but they certainly sounded a lot less certain than Greenspan that productivity would slow significantly or that hiring would be robust.

Other economists agree, citing a host of factors -- such as anemic corporate pricing power, high health-care costs and tax incentives -- that could keep businesses spending on new technology, rather than in workers, for much of the year.

"Firms in the past year have continued to invest in equipment and technology to improve productivity," said former Fed economist Wayne Ayers, now chief economist at Fleet Boston Financial. "And with good reason -- the cost of capital is below the cost of labor."

"I don't think there's much of a chance we will see anything more than moderate job growth, at least through the first half of the year," he added.

The question, then, could be how much a slowly recovering labor market affects the broader economy. Last week, the University of Michigan's consumer sentiment index posted a surprising decline, in part because of lingering concerns about jobs.

Still, confidence was much higher than it was when layoffs jumped last year, and slow but steady job growth could be enough to keep consumers -- whose spending fuels two-thirds of the economy -- hanging in there.

"I think the employment situation is getting better, slowly, so I don't think it will cause the consumer to shut down," said former Fed economist Lara Rhame, now at Brown Brothers Harriman. "But job growth like this makes consumer spending that much more fragile, if some exogenous shock should hit."