* Prices fall before first of $72 bln new debt sales * Spending cuts due in March may increase demand for bonds * Barclays sees 10-year yields falling to 1.80 percent By Karen Brettell NEW YORK, Feb 12 (Reuters) - U.S. Treasuries prices fell on Tuesday as dealers and investors prepared to absorb $72 billion in new debt supply this week. Investors are also increasingly turning their focus to the so-called "sequestration" spending cuts that are due to kick in next month, unless Congress reaches a deal to avoid them, which may cap weakness in U.S. government bonds. The Treasury will sell $32 billion in three-year notes on Tuesday, its first sale of coupon debt this week, followed by $24 billion in 10-year notes on Wednesday and $16 billion in 30-year bonds on Thursday. "I think the market is trying to build a concession for the auction process," said Tom Tucci, head of Treasuries trading at CIBC in New York. Benchmark 10-year notes fell 3/32 in price to yield 1.99 percent, up from 1.97 percent late on Monday. The notes traded at yields of around 2.01 percent in the "when-issued" market, which indicates where traders expect the new notes to price. Tucci says the notes would represent good value at around 2.02 percent or 2.03 percent, which is the top of their recent trading range, noting that the approaching date of the "sequester" and continued Federal Reserve bond buying makes a break above this range unlikely in the near term. "SEQUESTRATION" COMPLACENCY? Analysts at Barclays see Treasuries yields as likely to fall in coming weeks as more investors focus on the probability that spending cuts will be implemented. "I think there has been a lot of complacency. It would be a 30 basis point hit to GDP, which isn't really penciled in by a lot of people." said Rajiv Setia, head of U.S. rates research at Barclays in New York. The issue raises a dilemma for lawmakers as the implementation of the cuts threatens to slow economic growth, though the failure to stabilize the country's rising debt levels would increase the prospect of further U.S. ratings downgrades and pose longer-term problems for the economy. Treasuries yields surged in January after a last minute agreement to avoid the "fiscal cliff" spurred risk taking and reduced the safety demand for U.S. bonds, though Barclays sees this selloff as overdone. "The selloff in rates since the fiscal cliff deal has clearly overshot," said Setia. "I think we'll go through medium term austerity in the U.S. We are the only developed country that hasn't implemented a program." Benchmark 10-year notes yields jumped from 1.70 percent at year-end to as high as 2.06 percent on February 4, before falling back to 1.97 percent. Setia said that there is resistance at around 1.90 to 1.92 percent, and if yields drop below this level they are likely to fall further to around 1.80 percent. Barclays sees the notes ending the year at around 1.60 percent as investors adjust to slower growth than is currently projected. President Obama's State of the Union address will be closely watched later on Tuesday for signs of whether Congress is likely to reach a deal to avert cuts. Wednesday's retails sales data will also come under scrutiny to see if a payrolls tax hike that came into effect at the beginning of the year is weighing on consumer spending. The Federal Reserve will purchase between $2.75 billion and $3.50 billion in debt due 2020-2022 on Tuesday as part of its ongoing bond purchase program meant to stimulate the economy.