A report Tuesday, though, suggested that the data may well have been manipulated, though it's not as clear—as Welch charged—that political motivations were afoot.
An employee in the Census Bureau, under pressure to make the required amount of interviews to formulate the monthly nonfarm payrolls report, allegedly fabricated interviews that consequently made the unemployment rate slide from 8.1 percent to 7.8 percent, according to the New York Post.
That drop was highly consequential because it was the next-to-last reading on the jobs market before the November presidential election.
(Read more: Shutdown slowdown? Job creation soars in October)
Shortly after the numbers came out, the outspoken Welch attacked their veracity in a post on Twitter.
"Unbelievable jobs numbers...these Chicago guys will do anything...can't debate so change numbers," he tweeted then.
Reaction was swift and severe.
Former White House economist Austan Goolsbee tweeted to Welch, "you've lost your mind." Labor Secretary Hilda Solis called the charge "ridiculous." Reactions throughout much of the blogosphere were similar.
To be sure, Welch's accusations weren't especially specific, and the night before the Oct. 5 release he suggested that the data-fudging could pertain more to the labor force participation rate. He declined further comment through a spokeswoman Tuesday.
(Read more: Fake figures may have greased US jobs data: Report)
The Post's revelations, though, were no less shocking, in particular because the writer spoke to the actual Census Bureau employee who essentially admitted the numbers in the Philadelphia region had been manipulated.
"This seems to be completely unprecedented. I've never heard of this," said Alan Tonelson, research fellow at the U.S. Business and Industry Council in Washington. "It needs the most thorough investigation, ASAP."
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.
(Read more: Larry Summers and the never-ending bubble economy)
"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 @JeffCoxCNBCcom.