WASHINGTON — A sharp, unexpected drop in the unemployment rate Friday to 7.8 percent, a 44-month low, threatened to shake up the race for the White House and put the obscure Bureau of Labor Statistics in the crossfire amid unsubstantiated claims that the employment numbers are being cooked.

Coming weeks ahead of the Nov. 6 election, the Labor Department said employers added 114,000 jobs numbers in September and that the unemployment rate fell three-tenths of a percentage point. It was the first time since February 2009 that the jobless rate dropped below 8 percent, a tad lower than the 7.9 percent logged when President Barack Obama took office in January 2009.

“The jobs numbers were unambiguously positive. Job growth was solid; the gains were broad based across industries. Hours were up, as was wage growth,” said Mark Zandi, the chief economist for forecaster Moody’s Analytics. “The decline in the unemployment rate overstates the case, but a strong case can be made that the job market and economy are steadily improving.”

Democrats, who’ve been subdued in recent months amid sluggish jobs reports, lauded the news.

GOP presidential candidate Mitt Romney and other Republicans said the jobless rate was still too high.

“This is not what a real recovery looks like. We created fewer jobs in September than in August, and fewer jobs in August than in July,” Romney said in a statement.

At a campaign stop in Virginia, Obama accused Romney of downplaying good news. He said the jobs report “certainly is not an excuse to try to talk down the economy to score a few political points.”

During his own campaign swing later in Abingdon, Va., Romney suggested that there was less to the numbers than met the eye.

“So it looks like unemployment is getting better, but the truth is, if the same share of people were participating in the work force today as on the day the president got elected, our unemployment rate would be around 11 percent. That’s the real reality of what’s happening out there.”

Friday brought an unusual controversy over the numbers.

Jack Welch, the iconic business guru and former head of General Electric, who supports Romney, all but accused the Obama administration of cooking the books on economic statistics to boost the president’s prospects for re-election right after he fared poorly in the kickoff presidential debate earlier this week.

“Unbelievable jobs numbers,” Welch said on Twitter. “These Chicago guys will do anything … can’t debate so change numbers.”

Labor Secretary Hilda Solis, appearing on CNBC, dismissed the allegation as “ludicrous.”

Keith Hall, a former commissioner of the Bureau of Labor Statistics, also dismissed the charge.

“People shouldn’t think at all there is any bias in the numbers,” Hall, who’s now a senior scholar at George Mason University’s Mercatus Center, told McClatchy Newspapers. “This data is collected and examined by each state. … Hundreds of people at BLS help collect this data and compile it. If you wanted to try to mess with these numbers, you are talking a very difficult thing. It almost certainly would … be next to impossible.”

Yet in a sign that the economy remains below par, the number of long-term unemployed — those jobless for 27 weeks or more — remained stuck in September at 4.8 million. These long-term unemployed Americans accounted for 40.1 percent of all the jobless.