TREASURIES-Prices gain as higher yields lure buyers

* After selloff, higher yields attract buying

* Treasury to auction $32 bln in 3-yr notes

* Fed will buy $3 bln-$3.75 bln in notes due 2018-2019

NEW YORK, Jan 8 (Reuters) - U.S. Treasuries prices gained on Tuesday as some investors were drawn back into the debt by higher yields, and as investors prepared for the first sale of coupon-bearing Treasury debt for the year. Treasuries have sold off dramatically over the past week after lawmakers made concessions in order to avoid the "fiscal cliff" of tax hikes and spending cuts, reducing the safety bid for U.S. bonds. Market participants have also been debating whether the Fed is likely to end its bond purchase program before year end, after minutes from the Fed's December policy meeting released last week showed discord among Fed voting members on continuing the buybacks. The higher yields are likely to help demand for $66 billion in new debt sales this week. "The recent back up creates a buying opportunity," said Sean Simko, portfolio manager at SEI Investments in Oaks, Pennsylvania. 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 Treasures were last up 4/32 in price to yield 1.89 percent, down from 1.90 percent late on Monday, but up from around 1.70 percent at year-end. Thirty-year bonds gained 11/32 in price to yield 3.08 percent, down from 3.10 percent on Monday, and up from 2.87 percent at year-end. With no large economic indicators on the horizon, Treasuries are expected to stay largely rangebound, albeit in a higher yield range after the past week's push higher. The next focus for the market is likely to be a new round of wrestling in Washington where lawmakers face tough battles on how to cut spending and reduce the deficit, as the country also pushes up against its debt ceiling. "People are focusing back on the bigger picture, we still have the debt ceiling in front of us, we still have growth but albeit at a slower pace than everybody would like," said Simko. The Fed will buy between $3 billion and $3.75 billion in notes due 2018 and 2019 on Tuesday as part of its latest quantitative easing program, meant to stimulate hiring by reducing long-term borrowing rates.