(Fixes typo in U.S. Treasury 10-year yield to 1.03% in 7th paragraph) By Gertrude Chavez-Dreyfuss NEW YORK, Jan 26 (Reuters) - U.S. Treasury yields were little changed to slightly higher in choppy trading on Tuesday, after hitting three-week lows on the long end of the curve, as investors remained cautious in the near term about the size of a proposed U.S. stimulus package as well as 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 modestly to 91.50 basis points. U.S. Senate Majority Leader Chuck Schumer said late on Monday that 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. "We think ultimately it"s going to be smaller than the $1.9 trillion," said Mike Chang, interest rates strategist at Citi in New York. "We have penciled in around $600 billion-$1 trillion. Timing is another issue, not just the size - how long it will take to get the whole thing through." In addition, there have been coronavirus vaccine delivery problems globally, especially in Europe. 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. Pfizer Inc said there would be a temporary impact on shipments of its vaccine in late January to early February. In mid-morning trading, the U.S. benchmark 10-year yield fell to 1.03%, from 1.04% late on Monday. It earlier fell to 1.026%, its lowest level since Jan. 6. U.S. 30-year yields slid to 1.7955% from Monday"s 1.799%, after earlier dropping to a three-week low of 1.786%. U.S. 20-year bond yields also weakened to a three-week trough and were last down at 1.59%. On the front end of the curve, U.S. two-year yields slipped to 0.121% from 0.127% on Monday. Also on Tuesday, the Treasury auctions a record $61 billion in 5-year notes after a solid 2-year debt sale on Monday. "We believe there will be demand as the Treasury market has had a firm tone in recent sessions," Justin Lederer, rates strategist at Cantor Fitzgerald, said in a research note. "We, however, would not be surprised by a small back-up leading into 1 pm (bid deadline) and/or small tail as market participants are cautious at the current yield levels, as the sector is trading at its richest levels since early January and 12 basis points lower than its high yield print a few weeks ago," he added. Ahead of the auction, U.S. five-year note yields were little changed at 0.4119%. January 26 Tuesday 10:28AM New York / 1528 GMT Price Current Net Yield % Change (bps) Three-month bills 0.08 0.0811 0.000 Six-month bills 0.085 0.0862 -0.003 Two-year note 100-1/256 0.123 -0.004 Three-year note 99-214/256 0.1805 0.000 Five-year note 99-210/256 0.4119 0.002 Seven-year note 99-80/256 0.727 0.002 10-year note 98-116/256 1.0414 0.001 20-year bond 96-12/256 1.6089 0.005 30-year bond 95-236/256 1.8024 0.003 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 10.00 0.50 spread U.S. 10-year dollar swap 3.25 0.25 spread U.S. 30-year dollar swap -24.00 0.00 spread (Reporting by Gertrude Chavez-Dreyfuss Editing by Paul Simao)