* ADP employment misses forecast, factory orders drop * Housing stocks near four-year high * Chesapeake Energy shares tumble 15 pct * Dow off 0.1 pct, S&P off 0.3 pct, Nasdaq up 0.3 pct By Edward Krudy NEW YORK, May 2 (Reuters) - The S&P 500 and the Dow edged lower o n W ednesday as data showed that private sector hiring fell far more than expected in April, sparking concerns that Friday's U.S. jobs report will also disappoint investors. Private employers added 119,000 jobs in April, well short of the 177,000 expected, the ADP report showed. That sparked market rumors that Friday's payrolls data will show the economy added just 125,000 to 150,000 jobs last month, well below a Reuters consensus forecast of 170,000. "If fewer and fewer people are participating in this recovery it suggests underlying weakness that we have to address, and so far policymakers' answers have been 'easy credit' - I think we need to go beyond that," said Jack Ablin, chief investment officer at Harris Private Bank in Chicago. The report came on the heels of more glum news from Europe.