* U.S. yield curve steepens modestly * Near term, 10-year yield likely between 1.75%-2% -BofA * U.S. 5-year note auction shows mixed results * U.S. 5-year TIPS yield falls to lowest since April 2014 (Adds new comment, U.S. 5-year TIPS, updates prices) By Gertrude Chavez-Dreyfuss NEW YORK, Jan 26 (Reuters) - U.S. Treasury yields were mostly down in choppy trading on Tuesday, after earlier hitting three-week lows on the long end of the curve, as investors remained cautious about the size of a proposed U.S. stimulus package. The Federal Reserve also began its two-day policy gathering on Tuesday and will announce the results of its meeting on Wednesday. Analysts expect the Fed to stick to its dovish tone amid a persistent surge in virus cases. The U.S yield curve, meanwhile, steepened modestly after flattening on Monday. The spread between U.S. two-year and 10-year yields widened slightly to 91.30 basis points . Overall this month, the market has retraced some of the rise in yields that took those on the 10-year to their highest level since March last year. "Our read on the market remains a period of consolidation followed by another bullish flattening into month-end. This might get us comfortably through a non-event Fed," said BMO in a research note. U.S. Senate Majority Leader Chuck Schumer said late Monday he and his fellow Democrats may try to pass much of President Joe Biden"s $1.9 trillion coronavirus relief bill using a process that would bypass a Republican filibuster and could allow it to pass with a majority vote. That has dented optimism on the idea that the whole stimulus package would pass through Congress successfully. In late afternoon trading, the benchmark 10-year yield slipped to 1.034%, from 1.04% late on Monday. It earlier slid to 1.026%, its lowest level since Jan. 6. "We are clearly in the early expansion phase of the cycle," said BoFA Securities in a note on Tuesday. "The bearish momentum at the back-end of the curve is supported by improved fundamentals, while the front-end continues to be anchored by the Fed." In the early stage of the cycle, the bank said the 10-year yield is likely to trade in a range of 1.75-2%, while the two-year/10-year yield curve could widen to 150 basis points. U.S. 30-year yields were at 1.797% from Monday"s 1.799%, after earlier dropping to a three-week low of 1.786%. Also on Tuesday, the Treasury auctioned a record $61 billion in 5-year notes, with mixed results. A high yield of 0.424% - slightly lower than the "when-issued" or consensus forecast of 0.427% - suggested that investors were willing to buy the paper even at a lower yield than the consensus estimate. But the bid-to-cover ratio, a gauge of demand, was 2.34, below last month"s 2.39 and the 2.47 average, and the weakest since July largely due to the increased issue size, Action Economics said in its blog after the auction. Post-auction, U.S. five-year note yields were slightly up at 0.41%. In the Treasury Inflation Protected Securities (TIPS) market, the yield on U.S. five-year TIPS fell to -1.803% , its lowest yield since October 2004. That takes the 5-year breakeven rate to 2.17%, the expected average inflation rate over the next five years, and near its highest level since April 2014. January 26 Tuesday 4:19PM New York / 2119 GMT Price Current Net Yield % Change (bps) Three-month bills 0.0775 0.0786 -0.002 Six-month bills 0.085 0.0862 -0.003 Two-year note 100-2/256 0.1211 -0.006 Three-year note 99-216/256 0.1778 -0.002 Five-year note 99-214/256 0.4087 -0.001 Seven-year note 99-86/256 0.7235 -0.002 10-year note 98-128/256 1.0364 -0.004 20-year bond 96-40/256 1.6023 -0.002 30-year bond 96-28/256 1.7941 -0.005 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 7.50 -0.25 spread U.S. 3-year dollar swap 8.25 0.25 spread U.S. 5-year dollar swap 9.75 0.25 spread U.S. 10-year dollar swap 3.25 0.25 spread U.S. 30-year dollar swap -24.50 -0.50 spread (Reporting by Gertrude Chavez-Dreyfuss in New York Editing by Sonya Hepinstall and Matthew Lewis)