* Senate leader Reid hints U.S. might go over 'fiscal cliff' * U.S. fast approaching debt ceiling, Geithner tells Congress * January T-bill interest rates briefly turn negative By Chris Reese NEW YORK, Dec 27 (Reuters) - U.S. Treasury debt prices rose on Thursday on safe-haven buying after the Senate majority leader hinted a federal budget deal was unlikely before a year-end deadline, raising chances of a burdensome package of tax hikes and spending cuts next year. This series of automatic fiscal maneuvers worth $600 billion, commonly referred to as the "fiscal cliff," is set to phase in after Monday, raising fears of a U.S. recession. "It looks like that is where we're headed," Harry Reid, the Democrat leader of the Senate, said of the likelihood of the U.S. economy going over the "fiscal cliff." Nervous investors sold stocks and other risky assets and bought into Treasuries, sending the interest rates on T-bills for delivery in early January briefly into negative territory in reaction to Reid's glum assessment. "With each passing moment, investors take a step closer to the reality of a 'no deal' situation, which likely means that taking risk off the table is the proper action," said Kevin Giddis, head of fixed income capital markets at Morgan Keegan in Memphis, Tennessee. "This means that Treasury prices are going up and equity prices are going down as the risk 'shift' trade increases." Treasuries pared price gains, and stocks pulled back from sharp losses on Thursday afternoon after news the U.S. House of Representatives will hold a work session on Sunday beginning at 6:30 p.m. EST (2330 GMT), a day before the Dec. 31 deadline for reaching a deal to avert the "fiscal cliff." However, many analysts said chances have faded that a timely budget compromise will materialize and said the bond market is poised for further gains after Reid's pessimistic remarks. "That's probable if it looks like we're going over and there's still no agreement in sight," said Richard Gilhooly, interest rates strategist at TD Securities in New York. Benchmark 10-year notes traded 8/32 higher in price to yield 1.72 percent, down from 1.75 percent late Wednesday. Yields dipped to 1.70 percent early on Thursday afternoon, marking the lowest in nearly two weeks. Thirty-year bonds traded 17/32 higher in price to yield 2.89 percent, down from 2.92 percent late Wednesday. Among T-bills, interest rates on issues due in the first half of January were quoted on Thursday morning at minus 0.25 to 0.50 basis points. Trading volume rose from earlier in the week as most European markets reopened after the Christmas holiday, but it remained well below average. Anxiety about a possible recession if the U.S. goes over the 'fiscal cliff' overshadowed news that jobless claims fell to a near 4-1/2-year low and November new home sales rose to their highest since April 2010. Those positive readings were mitigated by a deterioration in consumer confidence, which fell to its weakest in four months in December. In addition to being the deadline on the fiscal cliff, Monday marks the day the federal government is set to reach its $16.4 trillion debt limit, the Treasury Department said late Wednesday. To cut government spending and delay bumping up against the debt ceiling, the Treasury will suspend issuance of state and local government series securities -- known as "slugs" -- beginning on Friday, Treasury Secretary Tim Geithner wrote in a letter to Congressional leaders. The Treasury will take other measures to buy time for the government to approve a debt ceiling increase. This scenario echoed what happened in the summer of 2011 when there was a stalemate between the White House and Congress on raising the federal debt limit and fears grew over a U.S. default. While Standard & Poor's at the time stripped the U.S. of its top-notch credit rating, Treasuries prices quickly recovered from losses after the debt ceiling was raised.