* U.S. and Greece budget concerns underpin bids for bonds * Traders shrug off U.S. durables, consumer data * U.S. to sell $35 billion in new two-year notes By Richard Leong NEW YORK, Nov 27 (Reuters) - U.S. government debt prices were little changed in choppy trading on Tuesday before a $35 billion auction of two-year notes, part of this week's $99 billion short-to-medium term dated bond supply. Persistent worries about the lack of progress in negotiations in Washington to avert a fiscal crisis offset bond selling to make room for this week's supply, analysts said. The absence of a budget compromise between President Barack Obama and federal lawmakers would cause a series of automatic tax hikes and spending cuts in early 2013 that may reduce the budget deficit but also tip the world's biggest economy into recession. "The market is pricing in a slow growth environment, even negative growth," said Anthony Valeri, fixed income strategist with LPL Financial in San Diego. On below-average trading volume, benchmark 10-year Treasury notes were up 2/32 in price at 99-22/32, yielding 1.659 percent, down 0.7 basis point from Monday. The 10-year yield has been stuck in the middle of its recent trading range. The 30-year bond last traded 1/32 lower at 98-29/32 to yield 2.804 percent, up 0.1 basis point on the day. Uneasiness about Greece and the United States overshadowed somewhat better-than-expected data on the U.S. economy. Some economists played down their significance since some indicators were measured before superstorm Sandy pummeled the Northeastern United States a month ago, disrupting business. Longer-dated bond prices tested their session highs earlier on a brief weakness in Wall Street stocks and the Federal Reserve's latest purchase of debt for its "Operation Twist." The three major U.S. stock indexes were steady midday with the Standard & Poor's 500 up 0.19 percent. The bond market retraced overnight losses linked to news that international lenders agreed to a debt relief deal for Greece so it will obtain more financial aid to avoid a messy default, analysts said. They said the selloff in bonds faded when traders grew skeptical over the lack of details on how Greece will carry out budget reforms needed to meet its new debt targets. "Their debt levels are still way too high," said Bret Barker, portfolio manager at TCW Group in Los Angeles. The market also had several indicators on the health of the U.S. economy to digest. Durable orders came in unchanged in October, less weak than a 0.6 percent fall predicted by economists. Home prices in 20 major U.S. cities grew 0.4 percent in September, reinforcing the view of an improving real estate sector, the Standard & Poor's/Case-Shiller report released on Tuesday showed. Americans' optimism on the economy rose to its highest level in more than four years in November, according to the Conference Board Without a shift in perception about the economy, most of the day's trading were short-term plays driven by this week's Fed purchases of longer-dated debt and the government's auctions of $99 billion in short-to-medium term supply, analysts said. In "when-issued" trading, the two-year notes for sale at 1 p.m. (1800 GMT) were expected to clear at a yield of 0.2740 percent. The two-year auction in October fetched a "high" yield of 0.295 percent. The Treasury Department will sell $35 billion in five-year notes on Wednesday and $29 billion in seven-year debt on Thursday. Meanwhile, the Fed bought $1.9 billion in Treasuries due in Feb 2023 to May 2030. The U.S. central bank could buy up to $15 billion in federal debt the rest of the week in four separate operations.