* December payrolls much lower than expected, weather blamed
* Housing stocks rise as jobs report lowers 10-year yield
* Alcoa slides after results, Sears down on holiday sales
* Dow off 0.2 pct, S&P 500 off 0.04 pct, Nasdaq up 0.02 pct
NEW YORK, Jan 10 (Reuters) - U.S. stocks traded flat on Friday after the December payroll report came in much weaker than expected, raising new questions about both the strength of the economy and the aggressiveness of Federal Reserve stimulus.
Only 74,000 workers were hired last month, the smallest increase since January 2011, and significantly under the 196,000 that had been expected by analysts.
While the jobs report bucked the positive trend of recent employment data - including the ADP report and jobless claims - the setback was expected to be temporary amid signs that the number of hires may have been affected by cold weather.
Investors continue to assess economic data through the Fed's eyes as they try to gauge how quickly the central bank will reduce its market-friendly bond purchases. December was the first payroll report since the U.S. central bank announced that it was reining in the stimulus program.
"Since economic momentum had seemed to be picking up, there were real concerns that tapering would become more aggressive throughout the year - fears that this report have washed away," said Alec Young, global equity strategist at S&P Capital IQ in New York.
"People are hoping this is an anomaly, and it seems like it was related to the weather, but if it is a trend, then that is a real threat to GDP and corporate earnings growth."
Seven of the 10 S&P 500 sector indexes were lower, with utilities and telecoms among the few rising for the day. Both groups are considered defensive plays. Financial and energy shares were the weakest for the day; both are closely tied to the pace of economic growth.
The Dow Jones industrial average was down 33.43 points, or 0.20 percent, at 16,411.33. The Standard & Poor's 500 Index was down just 0.65 of a point, or 0.04 percent, at 1,837.48. The Nasdaq Composite Index was up only 0.66 of a point, or 0.02 percent, at 4,156.85.
For the week, the S&P 500 is up 0.3 percent, while the Nasdaq is up 0.6 percent. The Dow is down 0.4 percent.
The payrolls report drove the yield of the benchmark 10-year U.S. Treasury note lower, which boosted housing stocks. Lennar Corp rose 2.5 percent to $39.38 while D.R. Horton Inc slid 2.8 percent to $22.35. The PHLX housing index rose 1.3 percent.
Shares of Alcoa Inc fell 5.4 percent to $10.11 a day after the company reported a massive quarterly loss, hurt by recent declines in aluminum prices and a non-cash impairment charge on smelter acquisitions.
Only 5 percent of S&P 500 components have reported results so far, with half of them posting better-than-expected profits and 62.5 percent topping revenue forecasts. Historically, 63 percent beat profit estimates, while 61 percent beat on revenue.
Sears Holdings Corp shares fell 13.5 percent to $36.82 a day after the retailer reported steep declines in comparable-store sales at its Kmart and namesake U.S. chain in the crucial holiday season.
Target Corp said a massive payment card data breach that occurred during the first three weeks of the holiday shopping season affected up to 70 million people, more than double its previous estimate. Its stock slid 1 percent to $62.69.
Shares of trucking company YRC Worldwide tumbled 14.1 percent to $13.46, a day after sliding 16 percent, as workers represented by the Teamsters union rejected a contract extension that the company proposed, jeopardizing a plan to restructure its debt.