* No visible signs of progress in resolving "fiscal cliff" impasse * Doubts arise over whether Italy will continue economic reforms * Treasury to sell $66 bln of debt this week By Chris Reese NEW YORK, Dec 10 (Reuters) - U.S. Treasury debt prices rose on Monday on concerns over protracted budget negotiations in Washington, political rumblings in Italy and expectations for further monetary policy easing by the Federal Reserve. President Barack Obama and Republican Speaker of the House of Representatives John Boehner failed to reach an agreement on Sunday on ways to stop large-scale, automatic fiscal tightening from kicking in next year. Economists fear the "fiscal cliff" of $600 billion worth of tax increases and spending cuts could send the U.S. economy back into recession, dragging the rest of the world with it. Lawmakers only have a few weeks left to try to avert it. In Italy, Prime Minister Mario Monti on Saturday said he would resign once the budget for 2013 was approved. Monti was trusted by investors to bring down Italy's huge debt and is credited for stabilizing the country's bond markets. The announcement came after former Prime Minister Silvio Berlusconi's party withdrew support for Monti last week and he said he could run to become a premier for a fifth time. This raised fears Monti's successor may not continue his economic reforms and Italy may come to the forefront of the euro zone debt crisis again. Italy's borrowing costs rose and U.S. government debt yields dipped in safe-haven demand for the lower-risk assets. Benchmark 10-year Treasury notes were trading 5/32 higher in price to yield 1.61 percent, down from 1.62 percent late Friday, while 30-year bonds were 10/32 higher to yield 2.79 percent from 2.81 percent. Price gains were limited however, with some investors reluctant to aggressively push yields lower ahead of the sale of $32 billion of three-year notes on Tuesday, $21 billion of 10-year notes on Wednesday and $13 billion of 30-year bonds on Thursday. "With the lack of data today, the market will focus the equity market direction, news of the fiscal cliff, and the set-up for this week's supply of 3-year, 10-year, and 30-year paper," said Tom di Galoma, managing director at Navigate Advisors LLC in Stamford, Connecticut. A better-than-expected November jobs report on Friday did little to alter expectations that the U.S. Federal Reserve is likely to muster some additional bond buying plans at its two-day meeting which will end on Wednesday. Many investors expect the Fed to announce it will buy $45 billion per month of longer-dated Treasuries beginning in January to replace the current "Operation Twist" stimulus program which expires at the end of December. Under Operation Twist, the central bank is selling shorter-dated U.S. government debt and buying longer-dated Treasuries to extend the duration of its balance sheet.