* U.S. nonfarm payrolls show surprise 20,000 fall in Jan
* Revisions reveal deeper losses than previously thought
* Unemployment rate, at 9.7 pct, is lowest in five months
* Geithner downplays risk of a double-dip recession (Adds Geithner comments in paragraphs 11-13)
WASHINGTON, Feb 5 (Reuters) - The U.S. unemployment rate surprisingly fell to a five-month low of 9.7 percent in January and factory payrolls grew for the first time since 2007, hinting at a labor market recovery even though the economy lost 20,000 jobs.
President Barack Obama cautiously welcomed the figures but said more needed to be done to put people back to work. Obama and fellow Democrats fear voters could punish them in November congressional elections if no headway is made in tackling unemployment as the United States emerges from recession.
The decline in payrolls reported by the Labor Department on Friday was far smaller than the 150,000 drop posted in December. November's data from the survey of employers was revised sharply higher to a gain of 64,000, up from 4,000.
The jobless rate of 9.7 percent, based on a separate household survey, was lower than the 10 percent in December. That survey found employment rising, with the size of the labor force roughly flat.
Analysts had expected payrolls to rise by 5,000 and the unemployment rate to edge up to 10.1 percent.
"The wheels of the economy are turning. The improvement in the employment data does match the increase in GDP the last two quarters so it's not a fluke," said Chris Rupkey, senior financial economist at Bank of Tokyo/Mitsubishi UFJ in New York, referring to growth data for the fourth quarter of 2009.
"The economic recovery looks much more sustainable today."
Details of the report were relatively upbeat. The length of the average workweek hit its highest in a year and overtime paid in manufacturing was the most since September 2008, suggesting growing pressure to add to payrolls.
But some analysts were skeptical of the drop in the jobless rate and believed it would head higher again. The pickup in factory employment helped to lift U.S. stocks, despite lingering worries about European fiscal problems.
U.S. government debt prices rose and the U.S. dollar hit an 8-1/2 month high versus the euro, tapping flight-to-quality trades from the troubles in Europe.
Treasury Secretary Tim Geithner downplayed the possibility of a double-dip recession.
"We have much, much lower risk of that today than at any time over the last 12 months or so," Geithner said in excerpts from an interview with ABC's Sunday morning news program "This Week."
"We are in an economy that was growing at the rate of almost 6 percent of GDP in the fourth quarter of last year, the most rapid rate in six years. So we are beginning the process of healing."
Annual revisions to the payrolls data showed job losses since the recession began were much deeper than originally thought. The economy has lost 8.4 million jobs since December 2007, compared with 7.2 million before the revisions.
In January, the number of "discouraged job seekers" stood at 1.1 million, up from 734,000 a year ago. Last month, 6.3 million people had been out of work of more than 27 weeks.
With Americans increasingly anxious about persistently high unemployment, Obama has declared that job creation will be his top priority in 2010. Announcing plans on Friday to expand credit for small businesses, Obama said the employment report was cause for hope but not celebration.
"Understanding that these numbers will continue to fluctuate for months to come, these are welcome, if modest signs of progress along the road to recovery," Obama said.
Financial markets have grown nervous about the prospect of unemployment in the United States remaining high for a long time. The economy resumed growth in the second half of 2009 but a labor market recovery has yet to materialize.
Labor market weakness is causing households to remain wary of taking on new debt, with total consumer credit declining by $1.73 billion in December, a Federal Reserve report showed.
While the U.S. economy is growing, recovery hopes in Germany were dealt a set back by a sharp drop in industrial output in December. For details see [ID:nLDE614128]
A survey of banks that do business with the Federal Reserve predicted the U.S. central bank will start raising interest rates in the fourth quarter of this year as the labor market mends.
Analysts expect U.S. payrolls to start growing in February as the government steps up temporary hiring for the 2010 census.
"This hiring will continue to push the unemployment rate lower and then once the need for these workers is finished they will be fired and the unemployment rate will drift back up to the 10 percent area," said Brian Fabbri, chief North America economist at BNP Paribas in New York.
Last month, the services sector added 40,000 jobs after shedding 96,000 positions in December. The figure included a rise in federal government employment, partly a result of early hiring for the census.
In another positive trend, temporary help employment rose again last month, while manufacturing payrolls increased 11,000, the first gain since January 2007. Manufacturing employment had dropped 23,000 in December.
But the construction sector continued to struggle, losing 75,000 jobs, likely because of unusually cold weather. Construction payrolls fell 32,000 in December.
In another sign of labor market improvement, the average workweek unexpectedly edged up to 33.3 hours, the highest in a year, from 33.2 hours in December, while manufacturing overtime rose to 3.5 hours, the highest since September 2008.
"This suggests that firms are straining to keep up with rising demand without hiring," said Stephen Stanley, chief economist at RBS in Stamford, Connecticut.
"We believe that as long as orders keep streaming in, at some point soon firms are going to have to give in and add workers." For graphic on earnings and the workweek see: link.reuters.com/wyw87h For graphic on benchmark revisions see: link.reuters.com/sav87h (Additional reporting by the White House team; Editing by John O'Callaghan)