* U.S. private sector adds 198,000 jobs in February * 10-year yields at highest in more than a week * U.S. non-farm payroll data due on Friday By Chris Reese NEW YORK, March 6 (Reuters) - U.S. Treasuries prices fell for a third consecutive session on Wednesday as better-than-expected jobs data undermined the safe-haven allure of U.S. government debt, and as investors set up for new debt supply next week. Losses were limited, however, by expectations the Federal Reserve will continue buying debt through the year in an effort to prop up the economy, while a drop in new orders for factory goods underscored the still-modest pace of recovery in the world's largest economy. Treasuries have slid recently as investors, expecting low interest rates for years to come, have sought returns in riskier assets such as stocks, boosting the Dow Jones Industrial Average on Tuesday to an all-time high. That index rose again on Wednesday, surpassing the previous session's record. A report by payrolls processor ADP showed U.S. private employers added 198,000 jobs in February, which was more than expected and taken by investors as another sign of improvement in the labor market. The report bolstered some expectations the government could report relatively solid jobs growth in February non-farm payrolls data, due on Friday. Friday's number is particularly important because Federal Reserve policy makers want the U.S. jobless rate to fall from its current 7.9 percent level closer to 6.5 percent. "Ever since the Fed has tied its guidance on interest rates and quantitative easing to labor market data, that has been where the market has been focused as well," said Jake Lowery, Treasury trader at ING Investment Management in Atlanta. "We had ADP employment data today, which surprised to the upside, and that helped take (Treasuries) rates higher." Anticipation of next week's Treasuries supply also tugged at prices, Lowery said. The U.S. Treasury is set to auction three-year and 10-year notes next week, along with 30-year bonds. "It seems that with Treasuries trading in a pretty tight range lately, more and more market participants are focusing on small opportunities around the supply calendar each month, and some people are trying to set up for that supply even before payrolls," he said. Benchmark 10-year Treasury notes traded 12/32 lower in price to yield 1.94 percent, the highest in over a week and up from 1.90 percent late Tuesday. Thirty-year bonds traded 27/32 lower to yield 3.15 percent from 3.11 percent. In addition to the private employment data on Wednesday, data also showed new orders for U.S. factory goods fell in January as demand for transportation equipment weakened, but the underlying strength in manufacturing remained intact. Stephen Stanley, chief economist with Pierpont Securities in Stamford, Connecticut, said that what Fed Chairman Ben Bernanke and vice-chair Janet Yellen have said recently about asset purchases, "have pushed the timetable out." Stanley said he expects the U.S. central bank's unconventional monetary policy, known as quantitative easing, to end early next year. The Fed's support has helped fuel the recent stock rally, with the central bank buying $85 billion per month of mortgage-backed securities and Treasuries in an open-ended program that is generally expected to last through 2013.