Whether that will happen is unclear, though the Department of Commerce's Inspector General's Office issued a statement to CNBC saying, "We are aware of the media reports and our office is evaluating what actions may be warranted."
For its part, the Census Bureau said it does not believe there has been any "systematic" manipulation of data, stressing its vigorous process of double-checking to make sure the information it provides is correct.
That monitoring process includes re-interviewing respondents, and rechecking the data an employee has submitted, looking for red flags that indicate possible fabrication, such as abnormally short lengths of interviews or higher survey completion rates that are out of sync with normal survey collection productivity levels," the bureau said in a statement. "That is why when we learned of the allegations of fabricated Current Population survey results, we immediately reported them to the Office of the Inspector General."
Should the controversy go full-blown, it could shake the government's data-gathering operations at their foundation.
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"The problem is the financial markets are already pretty cynical. If there is any case in which this is proven that the data were not done in a satisfactory, compliant way, then markets are going to have more reason not to believe the figures," said Joe LaVorgna, chief U.S. economist at Deutsche Bank. "When they move in any direction that is counter to expectations, it will be one of those see-I-told-you-so moments."
The jobless count in particular has come under scrutiny in part because the unemployment rate has been declining primarily through a reduction in the labor force.
In the September 2010 count, the participation rate held steady, but there were other startling numbers that quickly generated skepticism.
Total employment for the month soared by 873,000 after being essentially flat the previous three months. Job losers decreased by 468,000, and short-term unemployment fell by 302,000. Finally, those working part-time for economic reasons surged from 8 million to 8.6 million.
"We didn't think the numbers were accurate, but not for the reasons the (Post) article suggested," LaVorgna said.
(Read more: US labor costs point to still-benign inflation)
The controversy likely will feed the fire over how much investors should rely on the data.
In addition to the jobless count, critics often wonder why the government strips out gas and grocery prices when it announces the so-called core Consumer Price Index, and retail sales numbers have long been the target of questioning as well.
Economist Michael Pento said the controversy is a reminder that investors should not judge economic conditions through a single month's numbers.
"You have to look for long-term trends in the data," said Pento, head of Pento Portfolio Strategies. "The (employment-to-population ratio) and labor force participation rate both popped in 2008 and have never recovered. That tells me the labor force is anemic."
—By CNBC's Jeff Cox. Follow him on Twitter