* U.S. 3-year note sale shows solid demand * U.S. yield curve steepens; spread widest since June * U.S. curve pricing more fiscal spending, Biden win (Adds new comment, 3-year auction results, updates prices) By Gertrude Chavez-Dreyfuss NEW YORK, Oct 6 (Reuters) - U.S. long-dated Treasury yields climbed to four-month peaks on Tuesday as investors sold government debt ahead of heavy supply this week and priced in the prospect of a victory by Democratic challenger Joe Biden in next month"s U.S. presidential election. The U.S. Treasury"s record $52 billion auction of three-year notes on Tuesday showed decent demand, even though the yield was a little higher than what was expected at the bid deadline. The Treasury will sell $35 billion in 10-year notes on Wednesday and $23 billion 20-year bonds on Thursday, which analysts said could be the true test of demand for U.S. debt. U.S. 10-year, 20-year and 30-year yields rose to their highest level since June, while the yield curve steepened again. The spread of two-year and 10-year yields hit its widest since June, while that between the five-year and 30-year reached 127 basis points, the largest gap since early June as well. By the afternoon session, the curve had flattened a bit. A steeper curve suggests expectations of higher growth and inflation. "I think there is a lot of fundamentals out there that support a steeper curve, whether that"s increased issuance from the Treasury, or increased supply as a whole," said Patrick Leary, chief market strategist and senior trader, at Incapital. "The bigger issue is all the stimulus, all that pent-up U.S. savings, which are at an all-time high right now. The amount of spending that can be unleashed in this market is massive and that can have a stimulative, growth, and inflationary effect," Leary added. The steeper curve continued to price in a Biden victory over President Donald Trump in the Nov. 3 election, analysts said. A victory for Biden and a Democratic sweep in Congress would mean higher fiscal spending and more Treasury supply, said Jon Hill, senior rates strategist, at BMO Capital in New York. Biden opened his widest lead in a month after Trump"s positive coronavirus test as a majority of Americans believed the Republican president could have avoided the infection if he had taken the virus more seriously, the latest Reuters/Ipsos poll showed. In afternoon trading, U.S. 10-year yields rose to 0.773%, from 0.762% late on Monday, after earlier rising to 0.792%, the highest level since June. Yields on U.S. 30-year bonds were at 1.585%, up from 1.567% on Monday. Earlier, 30-year yields climbed to a four-month peak of 1.61%. The yield curve steepened on Tuesday as well, with the spread between the 10-year and two-year widening to as much as 64.5 basis points, the widest spread since June. By the afternoon session, the spread had declined to 61.70 basis points. Treasury"s sale of U.S. three-year notes on Tuesday was solid given the record size, analysts said, with the bid-to-cover ratio of 2.44 higher than 2.28 last month. October 6 Tuesday 2:40 PM New York / 1840 GMT Price Current Net Yield % Change (bps) Three-month bills 0.1 0.1014 0.002 Six-month bills 0.115 0.1167 0.003 Two-year note 99-243/256 0.1507 0.006 Three-year note 99-208/256 0.189 0.003 Five-year note 99-154/256 0.3307 0.007 Seven-year note 98-216/256 0.544 0.007 10-year note 98-152/256 0.7734 0.011 20-year bond 96-28/256 1.349 0.017 30-year bond 95-12/256 1.5838 0.017 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 8.25 0.25 spread U.S. 3-year dollar swap 7.75 0.50 spread U.S. 5-year dollar swap 6.50 0.00 spread U.S. 10-year dollar swap 1.50 0.00 spread U.S. 30-year dollar swap -37.75 -0.25 spread (Reporting by Gertrude Chavez-Dreyfuss Editing by Nick Zieminski and Will Dunham)