* Benchmark 10-year note yields lowest in two weeks * Fiscal, economic fears seen boosting Treasuries * Fed purchases $4.99 bln in last Twist buyback By Karen Brettell NEW YORK, Dec 28 (Reuters) - U.S. benchmark Treasuries yields fell to their lowest levels in two weeks on Friday as hopes faded for a deal to avoid tax hikes and spending cuts that could throw the U.S. economy into recession. Investors are focused on Washington as President Barack Obama and lawmakers launch a last-chance round of budget negotiations days before a New Year's deadline to reach a deal or watch the economy go off a "fiscal cliff." Window-dressing for year-end and month-end extension buying also boosted demand for Treasuries on the second last trading day of 2012. "The market has lost the optimism it had over a deal getting done, it was much more optimistic a week ago," said Jason Rogan, managing director in Treasuries trading at Guggenheim Partners in New York. Treasuries temporarily pared prices gains on Friday after President Obama was reported by news outlets including Bloomberg as saying he would offer a scaled back budget package today. "I still think it's unlikely that a deal will go through, but it seems like a step in the right direction so the market came off," said Sean Murphy, a Treasuries trader at Societe Generale in New York. Bonds then recaptured their price gains as the Federal Reserve bought $4.99 billion in notes due 2021 and 2022 in its final Operation Twist program, in which it buys long-term notes and funds the purchases with sales of short-term notes. The central bank will replace that operation next year with outright purchases of Treasuries from 5-years to 30-years as it seeks to boost spending and economic growth. Concerns that lawmakers will fail to reach a deal to resolve the fiscal crunch by year-end is expected to keep a bid for safe haven Treasuries in the coming days, or weeks. "I think the most likely scenario is that we will probably go over the cliff, there is a lot of posturing on both sides," said John Fath, managing partner at BTG Pactual in New York. Many investors expect that negotiations will extend beyond Monday's deadline, but that some kind of agreement is likely in the first few weeks of January. "There is the assumption that something will get done. As time continues to go on with no deal taking place I think you will start to see the market really start to get a flight-to-quality bid," said Guggenheim's Rogan. Some also fear that lawmakers are unlikely to reach a substantive consensus on how to reduce the U.S. deficit, with the most likely outcome that they will agree on smaller issues in early January and then push back negotiations on larger issues to later in 2013. This may also increase the risk of further negative actions on the U.S. credit rating. Treasuries rallied when Standard & Poor's cut the U.S. credit rating to the second highest investment grade in August 2011, though investors have said there's no certainty the market will react the same way a second time. "The kneejerk reaction is that there could be a move to flight-to-quality," said BTG's Fath. Longer term, "there might be a bit of an illusion in the marketplace, particularly with lawmakers, that it will have no effect or bearing on rates, but at some point it will." Fitch Ratings and Moody's Investors Service both rate the U.S. the top triple-A and all three major rating agencies have a negative outlook on the country. Benchmark 10-year notes were last up 7/32 in price, with yields falling to 1.71 percent, down from 1.73 percent on Thursday and from a two-month high of 1.85 percent a week and a half ago. Thirty-year bonds rose 12/32 in price to yield 2.89 percent, down from 2.90 percent on Thursday and the lowest since Dec. 17.