* 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 (Adds new comment, auction results, updates prices) By Gertrude Chavez-Dreyfuss NEW YORK, Jan 26 (Reuters) - U.S. Treasury yields were narrowly mixed in choppy trading on Tuesday, after 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 and the slow global roll-out of coronavirus vaccines. The U.S yield curve steepened modestly after flattening on Monday. The spread between U.S. two-year and 10-year yields widened slightly to 91.30 basis points. 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. Mike Chang, interest rates strategist at Citi in New York, said his firm believes the stimulus package would be much smaller, around $600 billion to $1 trillion. "Timing is another issue, not just the size - how long it will take to get the whole thing through," he added. In addition, there have been coronavirus vaccine delivery problems globally, especially in Europe. For instance, AstraZeneca, which developed its vaccine with Oxford University, told the European Union that it could not meet agreed supply targets by the end of March. In early afternoon trading, the benchmark 10-year yield slipped to 1.036%, from 1.04% late on Monday. It earlier slid to 1.026%, its lowest since Jan. 6. "We are clearly in the early expansion phase of the cycle," said BoFA Securities in a note on Tuesday. "With the (Federal Reserve) squarely on hold, the expectation is for a bear-steepening dynamic for the curve. 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 up at 1.801% from Monday"s 1.799%, after earlier dropping to a three-week low of 1.786%. On the front end of the curve, U.S. two-year yields slipped to 0.123% from 0.127% on Monday. 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 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 volume, Action Economics said in its blog after the auction. Post-auction, U.S. five-year note yields were slightly down at 0.408%. The Federal Reserve 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. January 26 Tuesday 2:03PM New York / 1903 GMT Price Current Net Yield % Change (bps) Three-month bills 0.0775 0.0786 -0.002 Six-month bills 0.0825 0.0837 -0.005 Two-year note 100-1/256 0.123 -0.004 Three-year note 99-214/256 0.1805 0.000 Five-year note 99-212/256 0.4103 0.000 Seven-year note 99-84/256 0.7246 0.000 10-year note 98-124/256 1.0381 -0.002 20-year bond 96-16/256 1.608 0.004 30-year bond 95-232/256 1.8031 0.004 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 8.00 0.00 spread U.S. 5-year dollar swap 9.75 0.25 spread U.S. 10-year dollar swap 3.00 0.00 spread U.S. 30-year dollar swap -24.75 -0.75 spread (Reporting by Gertrude Chavez-Dreyfuss; Editing by Paul Simao and Sonya Hepinstall)