* "Fiscal cliff" deadline only hours away * Some investors betting government can still reach a "cliff" deal * Yields well within a range that has held since early August By Chris Reese NEW YORK, Dec 31 (Reuters) - U.S. Treasury debt prices eased on Monday on some investor optimism that Washington officials might complete a last-minute deal to avert the "fiscal cliff" of tax increases and government spending cuts that could push the U.S. back into recession. Treasuries prices rose last week as worries over the impact of the "fiscal cliff" spurred safe-haven buying of U.S. government debt, but a few investors on Monday were betting the government could still come up with a plan to at least temporarily stave off some tax increases and spending cuts. The U.S. Congress comes back on Monday without a deal to avert the "fiscal cliff" and only a few hours of actual legislative time scheduled in which to act if an agreement materializes. "Talk of a last minute deal has driven the long-end more than half a point lower," said Richard Gilhooly, interest rates strategist at TD Securities in New York. Benchmark 10-year Treasury notes were trading 7/32 lower in price with their yield rising to 1.73 percent from 1.70 percent late Friday. Benchmark yields have gained 12 basis points since the beginning of December, and are on track for the biggest monthly rise since March. Benchmark yields are set to close out the year down 15 basis points from the end of 2011, but remain very near the middle of a range of 1.54 percent to 1.89 percent that has held since early August. "Treasuries remain in a holding pattern as the market awaits the results of the budget debates," said David Ader, head of government bond strategy at CRT Capital Group in Stamford, Connecticut. Thirty-year bonds were trading 22/32 lower in price to yield 2.90 percent, up from 2.87 percent late Friday. The Treasury market will close early at 2 p.m. EST (1900 GMT) on Monday ahead of the New Year's Day holiday on Tuesday.