* ADP Dec private employment rises by more than expected * Price losses limited by worries over coming political battle * Fed buying longer-dated Treasuries By Chris Reese NEW YORK, Jan 3 (Reuters) - U.S. Treasury debt prices were steady to slightly lower on Thursday after data showing the private sector added more jobs than expected in December, which undermined the safe-haven appeal of U.S. government debt. Yields briefly touched the three-month highs reached on Wednesday, when bonds sold off sharply 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 holdings as U.S. political battles loom in coming weeks over spending cuts and raising the nation's debt ceiling. Still, ahead of Friday's key 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 1/32 lower in price with their yield little changed from late Wednesday at 1.84 percent. Benchmark yields rose to 1.86 percent directly after the release of the ADP data, matching the three-month high touched on Wednesday on news the government had reached a last-minute agreement to avert the "fiscal cliff." President Barack Obama and congressional Republicans face two more months of tough talks on spending cuts and an increase in the nation's debt limit as the hard-fought deal to avert the so called "fiscal cliff" covered only taxes and delayed decisions on expenditure until March 1. Yields may rise further if data, including the closely watched jobs report for December due out on Friday, show the U.S. economy is improving. In the limited selling, one big buyer was scheduled in longer-dated debt. The Federal Reserve on Thursday will buy $4.25 billion to $5.25 billion of Treasuries maturing January 2017 through September 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.