* Investors focus on new supply this week * Bonds trade in higher yield range after selloff * Fed will buy $1.25-$1.75 bln in bonds due 2036-2042 on Monday By Karen Brettell NEW YORK, Jan 7 (Reuters) - U.S. Treasuries were steady on Monday as investors prepared for the first sale of new coupon-bearing debt this year and adjusted to a higher yield range after a dramatic selloff last week. Treasuries yields broke through support levels last week after the minutes from December's Federal Reserve meeting led some to speculate that the central bank may end its bond purchases before year-end, earlier than many thought. Despite the recent yield gains, new sales of $66 billion in new coupon-bearing debt this week will likely cap 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 unchanged to yield 1.90 percent. They have risen from 1.70 percent at year-end. After last week's selloff, Mulholland sees the notes now trading in a range from around 1.85 percent to 2.10 percent. A compromise struck by Congress last week to avert the worst of tax hikes and spending cuts has dampened demand for safe-haven bonds, though lawmakers face much tougher battles ahead over how to cut spending and resolve the gaping U.S. deficit. "The risk for the market will be the budget debate and how that goes, but that's a few weeks away now," Mulholland said. 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. On Monday it will purchase between $1.25 billion and $1.75 billion in bonds due from 2036 and 2042 on Monday as part of its quantitative easing program.