* Investors focus on $66 bln new supply this week * Bonds trade in higher yield range after sell-off * Fed buys $1.47 bln in bonds due 2036-2042 By Karen Brettell NEW YORK, Jan 7 U.S. Treasuries yields edged up on Monday as investors prepared for the first sale of new coupon-bearing debt this year and speculated on whether the Federal Reserve is likely to end bond purchases before year-end. Yields broke through support levels last week to trade at eight-month highs after the minutes from December's Fed meeting led some to speculate that the central bank may end its bond purchases earlier than many thought. Despite the recent yield gains, sales of $66 billion in new coupon-bearing debt this week may put a lid on any significant rallies from investors seeking to take advantage of the higher yields. "We have a lot of supply this week so I think the rallies will be somewhat capped," said Dan Mulholland, managing director in Treasuries trading at BNY Mellon in New York. The Treasury will sell $32 billion in three-year notes on Tuesday, $21 billion in 10-year notes on Wednesday and $13 billion in 30-year bonds on Thursday. Benchmark 10-year notes were last down 2/32 in price to yield 1.91 percent, up from 1.90 percent on Friday. They have risen from 1.70 percent at year-end. After last week's sell-off, Mulholland sees the notes trading in a range of around 1.85 percent to 2.10 percent. The dramatic increase in yields so far this year is raising the question of how far the sell-off will extend, with much debate over whether 2013 will be the year that finally ends the 30-year bond bull run. Societe Generale sees bond yields marching higher through the year, as economic data continues to improve. "Things are going to get better from here. I think we're already seeing momentum," said Mary Beth Fisher, head of rate strategy at the bank in New York. One wild card in the coming weeks is whether Treasuries will regain a safety bid as the U.S. Treasury again gets close to hitting the debt ceiling and as lawmakers wrangle over how to cut spending and reduce the gaping deficit. SocGen's Fisher sees yields in general heading higher, though she notes the market may become more volatile as negotiations get more heated. "The 'Fiscal Cliff: Part 2' negotiations are going to make the market volatile, but it won't substantially change its direction," she said. The bank recommends entering trades that would benefit from a steepening yield curve between three-year and 10-year notes to take advantage of an expected increase in volatility. The Federal Reserve will buy debt every day this week as part of its quantitative easing program, meant to hold down long-term borrowing rates in a bid to stimulate the economy. That may help hold down the longest part of the yield curve. "That may keep a flattening pressure on the market," said BNY's Mulholland. The Fed on Monday bought $1.47 billion in bonds due from 2036 to 2042.