* U.S. home prices grew modestly in Aug: Case-Shiller * U.S. consumer mood rosiest in 7 months-Conference Board * Report about ECB bond program spurs earlier bond bids * U.S. to sell $35 billion in new 2-year notes By Richard Leong NEW YORK, Sept 25 (Reuters) - U.S. government debt prices dipped on Tuesday, snapping a six-session winning streak, as encouraging U.S. housing and consumer data reduced worries about slowing global growth and counteracted anxiety about Europe's debt troubles. Traders and investors also sold bonds to make room for $35 billion in a two-year Treasuries sale this afternoon, part of this week's $99 billion in note offerings. "The market is positioning for this week's Treasuries supply," said John Canavan, market strategist at Stone & McCarthy Research Associates in Princeton, New Jersey. "We are also seeing a bit of improvement in the data." Despite lingering high unemployment, signs of a tentative recovery have arisen in the housing market and in the mood of shoppers. Home prices across 20 major U.S. cities showed a 1.2 percent year-over-year rise, S&P/Case-Shiller said on Tuesday. A growing belief in an improving housing sector might have boosted consumer confidence, which the Conference Board said rose to a seven-month high in September. More home building and sales should bode favorably for gross domestic product. Housing "will no longer be a drag on GDP going forward," said Dan Heckman, senior fixed income strategist at U.S. Bank Wealth Management in Minneapolis. "Things are not bad enough for yields to go much lower." Still worries about Europe's debt crisis worsening and hurting the global economy limited the decline in bond prices, analysts and traders said. The perceived stalling by Spain in asking for a full-blown financial rescue, together with fading optimism about more stimulus from the Federal Reserve and other major central banks, have underpinned a safehaven demand for Treasuries and German Bunds since last week. "Despite all the policy accommodation from major central banks, there is a question about global demand," said Larry Milstein, head of government and agency trading at R.W. Pressprich & Co in New York. Earlier, a German newspaper reported the European Central Bank and the German central bank are getting lawyers to verify the legality of the ECB's new bond purchase program. While it is unlikely such a move would scuttle the ECB's program, "it clearly causes more uncertainty," Milstein said. On Tuesday, benchmark 10-year notes were down 1/32 in price at 99-5/32, yielding 1.718 percent, up fractionally from Monday's close. Over the previous six sessions, U.S. and German government debt prices rebounded, recovering from a selloff in which the 10-year yield rose as high as 1.894 percent on Sept. 14, the day after the Fed said that it would buy $40 billion in mortgage-backed debt a month to bring down the country's stubbornly high unemployment rate. In Tuesday trade, the 30-year bond traded 4/32 lower at 96-29/32 to yield 2.907 percent, up 0.6 basis point from late Monday. Traders expect the upcoming two-year note issue to sell at a yield of 0.2750 percent, near the yield level at the two-year auction held in August. Treasuries slightly underperformed German Bunds, as their 10-year yield spread widened about 0.5 basis point to 15.4 basis points.