* Boehner, Obama remarks soothe some "fiscal cliff" worries * U.S. sells $35 billion of new five-year notes * Fed buys Treasuries in two operations * U.S. new home sales unexpectedly fall in October By Chris Reese NEW YORK, Nov 28 (Reuters) - A lack of progress in talks in Washington to avert a fiscal crisis mostly lifted U.S. government bond prices for a third straight day on Wednesday as the government sold $35 billon of five-year Treasury notes. Bond prices pulled back from earlier highs after U.S. House of Representatives Speaker John Boehner said he was "optimistic" on reaching a budget deal before the end of the year to avoid a crisis. President Barack Obama later said he hoped he and Congress can reach agreement before Christmas to avoid the "fiscal cliff" and shrink the budget deficit. But the market stayed in positive territory given the absence of specifics on how the two major political parties plan to arrive at a compromise on possible tax increases and spending cuts. Investors are worried gridlock between the White House and Congress over the series of automatic tax increases and spending cuts worth $600 billion that could phase in next year may well push the United States back into recession. Those worries have underpinned safe-haven support for the bond market since the U.S. presidential election three weeks ago. Investors dialed back hopes for a timely budget deal after Senate Majority Leader Harry Reid, a Democrat from Nevada, said on Tuesday he was disappointed there has been "little progress" in the negotiations. "Yesterday, it became clear that a quick resolution of the fiscal cliff is highly unlikely," said Christopher Low, chief economist at FTN Financial in New York. The Wednesday remarks from Boehner, the top Republican lawmaker, were similar in tone to what he has said previously, and the bond market remained skeptical a fiscal deal would be done before year-end. "There is some more optimism from (Boehner's) comments, but they still have not agreed on the details on how they will raise more revenues and how they will cut more spending, so there's a lot of work to be done," said Sean Incremona, senior economic analyst at 4Cast Ltd in New York. Safe-haven buying pushed benchmark 10-year Treasury notes up 6/32 in price to yield 1.62 percent, down from 1.64 percent late Tuesday and below the 100-day moving average near 1.65 percent. Trade volume was above average, according to data from Tradeweb. "Much of the bid continues to be a function of concerns that the fiscal cliff will prove more of a train wreck than an opportunity for bipartisan cooperation," said Ian Lyngen, senior government bond strategist at CRT Capital Group in Stamford, Connecticut. U.S. stocks reversed earlier losses after Boehner's remarks. They had hit session lows earlier after the government said new single-family home sales fell slightly in October and revised sharply lower its estimate for September sales, denting optimism over the housing market recovery, one of the brighter sectors of the economy. On the supply front, the Treasury Department continued its month-end sales of new short-to-medium-term debt, totaling $99 billion this week. It auctioned $35 billion in five-year notes at a high yield of 0.641 percent. The sale followed record demand for $35 billion of two-year notes on Tuesday. It will sell $29 billion of seven-year debt on Thursday. Meanwhile, the Federal Reserve bought conducted two separate purchases of Treasuries under its "Operation Twist" stimulus program, which is aimed at lowering long-term interest rates to help the economy. The Fed bought a total of $1.85 billion of Treasuries maturing in February 2036 through November 2042 in the first operation on Wednesday morning and then purchased $4.57 billion of Treasuries maturing November 2018 through November 2020 on Wednesday afternoon.