* U.S. private sector adds more jobs than expected in August * ECB announces unlimited bond buying program * U.S. weekly jobless claims come in lower than forecast By Chris Reese NEW YORK, Sept 6 (Reuters) - U.S. Treasuries prices fell on T hursday as the European Central Bank's announcement of a bond-buying program and higher-than-expected private sector U.S. jobs growth in August undermined the safe-haven appeal of U.S. government debt. ECB President Mario Draghi said the central bank will buy unlimited amounts of short-dated bonds to help lower the borrowing costs of Spain and Italy, which are bearing the brunt of the debt crisis in the euro zone. Draghi is looking to back up his July promise to do whatever it takes to preserve the euro. "Draghi with his debt purchase details this morning will move Europe from a bad to a good equilibrium," said Chris Rupkey, financial economist at Bank of Tokyo-Mitsubishi UFJ in New York. Separately, according to the ADP National Employment Report, U.S. private employers added 201,000 jobs in August, easily beating economists' expectations for 140,000 new private sector jobs. The jobs report boosted the outlook for the government's nonfarm payrolls data for August, to be released on Friday, and damped expectations for another round of economic stimulus from the Federal Reserve. The news from Europe, along with the U.S. jobs data, sapped the safety appeal of U.S. government debt, and benchmark 10-year Treasury notes traded 22/32 lower in price to yield 1.67 percent, up from 1.55 percent late Wednesday. Benchmark yields were trading at the highest in over a week, and the notes were on track for the biggest daily rise in yield in over three weeks. Lower-than-expected weekly claims for U.S. jobless benefits added to the bearish tone in Treasuries, as did data from the Institute for Supply Management showing the pace of growth in the U.S. services sector rose in August. "Today's U.S. reports all beat expectations to put a positive spin on the risks as we approach Friday's U.S. jobs data," said Michael Englund, chief economist at Action Economics in Boulder, Colorado. The median of forecasts from economists polled by Reuters is for U.S. employers to have added 125,000 jobs in August, down from 163,000 new hires in July. Thirty-year Treasury bonds were trading 1-2/32 lower in price to yield 2.76 percent from 2.71 percent late Wednesday.