* ADP Dec private employment rises by more than expected * Price losses limited by worries over coming political battle * Fed buys about $5.1 bln of longer-dated Treasuries By Chris Reese NEW YORK, Jan 3 (Reuters) - U.S. Treasury debt prices eased for a second session on Thursday, pushing yields to three-month highs after data showed the private sector added more jobs than expected in December, which undermined the safe-haven appeal of U.S. government debt. Treasuries had already sold off sharply on Wednesday following a U.S. government deal to avoid sharp tax hikes under the so-called "fiscal cliff." Thursday's losses were limited, however, with few investors willing to abandon lower-risk Treasury debt as U.S. political battles loom in coming weeks over spending cuts and raising the nation's debt ceiling. Still, ahead of Friday's December payrolls data from the government, investors were focused on the ADP Employment Report, which showed private-sector employers added 215,000 jobs in December. Economists surveyed by Reuters had been looking for a gain of 133,000 jobs. "There's an undeniable improving trend in the employment figures showing through in ADP and we've been seeing that in the non-farm private payrolls as well. That's in keeping with the overall picture of stable to improving growth that we saw as 2012 wound down," said Robert Tipp, chief investment strategist at Prudential Fixed Income in Newark, New Jersey. Good news for the economy is bad news for bonds, and benchmark 10-year Treasury notes traded 7/32 lower in price, their yield rising to 1.86 percent from 1.84 percent late on Wednesday. Benchmark yields traded as high as 1.87 percent on Thursday, the highest since mid-September, surpassing yield peaks touched on Wednesday on news the government had reached a last-minute agreement to avert the "fiscal cliff" of tax hikes and spending cuts that threatened to plunge the economy back into recession. President Barack Obama and congressional Republicans face two more months of tough talks, however, on spending cuts and an increase in the nation's debt limit as this week's hard-fought deal covered only taxes and delayed decisions on expenditure until March 1. In the limited selling, one big buyer offered a bit of support for Treasury debt prices. The Federal Reserve on Thursday bought about $5.1 billion of Treasuries maturing in 2017 in its first stimulus operation of the year. The central bank's "Operation Twist" stimulus program, under which it was selling shorter-dated Treasuries and buying longer-dated debt, expired at the end of December. The Fed is now buying about $40 billion per month of mortgage-backed securities and $45 billion per month of longer-dated Treasuries in an effort to prop up the economy. Some analysts have dubbed the Fed purchase programs "QE4." The Fed buying added to expectations Treasury yields might not have much room to rise over the short term, said George Goncalves, head of U.S. interest rates strategy at Nomura Securities International in New York. "Overall with ongoing political tension, non-stop Fed ... buying in QE4 throughout 2013, and a turn toward weaker data, U.S. Treasuries should be well supported in the weeks ahead and we continue to recommend buying on dips," Goncalves said. On the flip side, analysts said investors may be looking to cheapen Treasuries heading into the sale of $66 billion of government debt next week. The Treasury said on Thursday it will sell $32 billion of three-year notes, $21 billion of reopened 10-year notes and $13 billion of reopened 30-year bonds on Tuesday, Wednesday and Thursday respectively.