TREASURIES-Bonds fall in ongoing debt supply concerns

*Concern over raft of new debt supply again hits bonds

*Prices lower despite evidence of struggling employment

*Wave of supply includes Wednesday's 3-year note auction (Adds strategist comment, updates prices, adds byline)

By Chris Reese

NEW YORK, Jan 7 (Reuters) - U.S. Treasury debt prices fell on Wednesday over continued concerns that a spate of new debt supply will dilute the market, and despite more evidence of a dire U.S. employment situation.

A total of $166 billion of new government debt supply is on tap this week, with more expected in order to help feed various programs intended to prop up the economy.

Investors fear the huge doses of new debt issuance will have to boost Treasury note yields, which move inversely to prices and which remain not far off 50-year lows.

Treasuries briefly pared losses after the ADP Employer Services report said U.S. private employers shed 693,000 jobs in December, which was far more than economists had forecast and raised expectations the government's non-farm payrolls report, which will be released on Friday, will show a big drop in employment for December.

Still, the evidence of sinking employment was not enough to offset wariness over pending debt supply.

"There are still supply concerns out there," said David Coard, head of fixed income sales and trading at The Williams Capital Group in New York, adding "all that (ADP) does for me is confirm my expectations that we are going to get another doozy of a number on Friday."

Benchmark 10-year Treasury notes US10T=RR were trading 11/32 lower in price for a yield of 2.50 percent compared with 2.46 percent late on Tuesday, while the two-year note US2YT=RR was trading 3/32 lower with its yield rising to 0.82 percent from 0.78 percent.

Included in this week's wave of debt supply is the auction of $30 billion of three-year notes US3YT=RR on Wednesday afternoon, and then an auction of $16 billion of 10-year notes on Thursday afternoon.

Five-year notes US5YT=RR were trading 4/32 lower in price for a yield of 1.69 percent from 1.66 percent late on Tuesday, while the 30-year bond US30YT=RR was trading 1-5/32 lower in price for a yield of 3.05 percent from 3.00 percent. (Reporting by Chris Reese; Editing by Chizu Nomiyama)