TREASURIES-Bonds gain safety bid after Boehner tax plan fails

* Bond prices gain on renewed concern over "fiscal cliff"

* Yield curve flattens as Fed buys $1.89 billion in long bonds

* Volumes likely to drop as Christmas holiday, year-end approach

NEW YORK, Dec 21 (Reuters) - U.S. Treasuries gained a safety bid on Friday after House of Representatives Speak John Boehner failed to gain support for a tax plan, hurting stocks on concerns that lawmakers will be unable to reach a deal to avert the "fiscal cliff." The failure cast fresh uncertainty over talks to avoid roughly $600 billion in across-the-board tax hikes and automatic government spending cuts due to begin in January that could push the U.S. economy back into recession in 2013. The negotiations are expected to continue to dominate markets in the coming weeks, while trading volumes are expected to fall with the market closed next Tuesday for the Christmas holiday and as investors close books for year-end. "It's going to be all about whether things are being negotiated or not, what are the probabilities of us going over the cliff, are they getting worse or are they getting better," said Rick Klingman, a Treasuries trader at BNP Paribas in New York. Treasuries yields have fallen from two-month highs on Tuesday as doubts that lawmakers will reach a compromise increased. "Overall the 'risk on' mood from the last couple of weeks, with the thought process that something will get done in Washington, is being unwound a little bit," Klingman said. That trend may continue until there are fresh signs that a deal is more likely. The latest development "suggests the path of least resistance for stock prices and yields is going to be lower until it becomes clear that there really is a common-denominator-deal that can pass," said Robert Tipp, chief investment strategist with Prudential Fixed Income in Newark, New Jersey, which has about $350 billion in assets under management. The Treasuries yield curve also flattened on Friday as the Federal Reserve bought $1.89 billion in debt due from 2036 to 2042 as part of its Operation Twist program, designed to lower long-term borrowing rates. The yield gap between 30-year bonds and five-year notes narrowed to 218 basis points on Friday, the tightest in around three weeks. The Fed will buy additional bonds next Thursday and Friday as part of the operation, including up to $5.25 billion in notes due 2018 and 2020 on Thursday and up to $5.25 billion in notes due 2021-2022 on Friday. Benchmark 10-year notes were last up 13/32 in price to yield 1.76 percent, down from 1.80 percent late on Thursday. The yields have fallen from as high as 1.85 percent on Tuesday. Thirty-year bonds gained 1-3/32 in price to yield 2.93 percent, down from 2.98 percent late on Thursday.