* U.S. ADP jobs report in September was better than expected * U.S. yield curve flattens, reflects sooner than expected hike * Markets keeping an eye on debt ceiling as deadline looms (Recasts lead, adds fed funds futures, short-term bills; updates prices) By Gertrude Chavez-Dreyfuss and Tom Westbrook NEW YORK/SINGAPORE, Oct 6 (Reuters) - U.S. Treasury long-dated yields fell from more than three-month peaks on Wednesday, taking a respite from a sharp rise in recent sessions, as risk appetite took a tumble with the sell-off in stocks and commodities. The fall in long-end rates flattened the yield curve, with the spread between two-year and 10-year yields narrowing to 121.6 basis points after rising to 127 basis points, its widest since June. Some analysts said the flattening reflected expectations of an earlier-than-expected rate hike following strong U.S. private sector jobs data. An earlier report showing U.S. private payrolls increased more than expected in September to 568,000 jobs pushed Treasury yields higher. But that was short-lived as buyers stepped in to take advantage of Treasuries" oversold conditions. Since the private sector jobs data, Fed fund futures, which track short-term rate expectations, have priced in a 90% chance of a quarter-point hike by the Fed in November 2022, fully pricing that rate increase in December next year. That said, the outlook for longer-dated Treasury yields remained tilted to the upside amid optimism about U.S. growth and higher inflation expectations amid soaring energy prices. U.S. crude futures earlier hit an almost seven-year high on Wednesday amid a global fuel crunch that has unnerved markets and sent coal and natural gas prices soaring. But later on Wednesday, oil fell, triggering drops in coal and natural gas. Some traders said the collapse in these commodities may have triggered a sell-off in equities and a subsequent rally in Treasury debt prices, pulling yields lower. U.S. Treasury benchmark 10-year, 20-year and 30-year yields retreated from their June highs "We have said all year that 10-year yields should be in the 1.75% to 2% (range) by the end of the year," said Tony Rodriguez, head of fixed income strategy at Nuveen. "We"re kind of heading in that direction. Our view is that we"ll get to that level, but probably at the low end, given that over the summer, we saw some weakness related to the resurgence of COVID." The 10-year yield earlier in the global session rose to 1.573%, the highest since mid-June, but was subsequently down nearly 2 basis points at 1.5154%. Nominal yields have risen the last few weeks on expectation that the Federal Reserve will soon begin tapering asset purchases, and traders are awaiting more U.S. labor data, specifically Friday"s non-farm payrolls report, for clues as to the timing and tone of policy tightening. Yields on 20-year and 30-year Treasuries also jumped to their highest since June. In midday trading, 20-year yields were down nearly 2.9 basis points at 2.0155%, while those in 30-year bonds slid 3 basis points to 2.0697%. In the Treasury bills market, bills maturing on Oct. 19 and Oct. 21 showed elevated yields as high as 0.19% Senate Democrats are set to try again on Wednesday to extend the U.S. government"s borrowing authority to head off a catastrophic default, after President Joe Biden suggested they could change the chamber"s rules to bypass a Republican roadblock. "Right now, the premium you"re seeing in bills was not as high as the last time," said Nuveen"s Rodriguez. "We still think that Congress will, as it always will, raise the debt ceiling at the 11th hour." October 6 Wednesday 1:00PM New York / 1700 GMT Price Current Net Yield % Change (bps) Three-month bills 0.04 0.0406 0.000 Six-month bills 0.055 0.0558 0.000 Two-year note 99-231/256 0.2995 0.012 Three-year note 99-136/256 0.5359 0.014 Five-year note 99-124/256 0.9813 0.003 Seven-year note 99-156/256 1.3087 -0.006 10-year note 97-148/256 1.5154 -0.016 20-year bond 95-176/256 2.0145 -0.029 30-year bond 98-116/256 2.0697 -0.030 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 9.50 -0.25 spread U.S. 3-year dollar swap 12.75 -0.25 spread U.S. 5-year dollar swap 7.50 0.00 spread U.S. 10-year dollar swap 0.75 0.00 spread U.S. 30-year dollar swap -26.25 0.25 spread (Reporting by Gertrude Chavez-Dreyfuss in New York and Tom Westbrook in Singapore; Editing by Kim Coghill, Alison Williams and Mark Heinrich) Our Standards: The Thomson Reuters Trust Principles.