* U.S. 2/10 yield curve steepens * U.S. one-month T-bills stays elevated * U.S. Treasury"s Yellen presses Congress to lift debt ceiling * U.S. ISM-services index rises in September * Fed"s Evans says 3.5%-4% inflation this year a challenge (Adds new comment, Fed"s Evans remarks, ISM services index, byline, updates prices) By Karen Pierog and Gertrude Chavez-Dreyfuss CHICAGO/NEW YORK, Oct 5 (Reuters) - U.S. Treasury yields rose on Tuesday, as worries about the debt ceiling prompted investors to move away from the shortest end of the curve, while inflation concerns weighed on longer-dated debt. The yield curve, a gauge of economic sentiment and rate move expectations, steepened to 123.4 basis points, as measured by the spread between two-year and 10-year yields. That curve had steepened in six of the last nine sessions. "Bear steepeners are still driving the trade," said Kim Rupert, managing director, global fixed income analysis, at Action Economics in San Francisco. Bear steepeners reflect the market"s rising inflationary expectations. "There aren"t any new issues impacting, just the same old inflation with surging energy prices, supply chain disruptions, the debt limit and the threat of default." Chicago Federal Reserve Bank President Charles Evans, a known dove and a monetary policy voter this year, said he sees U.S. inflation to be 3.5% to 4% this year, which will be a challenge, but noted that it"s not a monetary policy issue. He also repeated his view, shared by most Fed policymakers, that the Fed is close to starting a reduction of its monthly asset purchases. In afternoon trading, the benchmark U.S. 10-year yield , which last week rose to its highest since June, was last up 5 basis points at 1.5327%. The yield on one-month Treasury bills, which on Monday shot up to 0.145%, the highest since October 2020, was last up at 0.1065%. Yields on the shortest end of the curve have been elevated as the U.S. Treasury eyes Oct. 18 as the date when it might run out of cash. In a CNBC interview on Tuesday, Treasury Secretary Janet Yellen said it was "utterly essential" to lift the debt ceiling to avoid a "catastrophic" default that would spark a recession and put the reserve status of the dollar at risk. Bill Merz, chief fixed income strategist at U.S. Bank Wealth Management, said yields on some Treasury bills were five times higher than they should be, as the chance of a technical default looms. "There"s zero incentive to hold those for most of the large buyers of T-bills so it"s understandable that they"re trading at a significant discount." The U.S. Senate is expected this week to take up a House-passed bill suspending the limit on Treasury borrowing through the end of 2022. Inflation expectations, meanwhile, jumped with the breakeven rate on five-year Treasury Inflation-Protected Securities (TIPS) rising to 2.61%, the highest since late July. The breakeven rate on 10-year TIPS hit 2.444%, the highest since early June. U.S. yields also nudged higher after data from the Institute for Supply Management showed U.S. services industry activity rose in September, although growth is being restrained by a persistent shortage of inputs and the resulting high prices as the pandemic drags on. The U.S. five-year note yield, which has become more sensitive to intermediate interest rate hikes, was last up 3.4 basis points at 0.9796%. October 5 Tuesday 3:06PM New York / 1906 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 99-237/256 0.2875 0.007 Three-year note 99-144/256 0.525 0.024 Five-year note 99-126/256 0.9796 0.034 Seven-year note 99-144/256 1.3158 0.045 10-year note 97-108/256 1.5327 0.052 20-year bond 95-52/256 2.0451 0.054 30-year bond 97-192/256 2.1018 0.054 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 9.75 0.50 spread U.S. 3-year dollar swap 13.00 -0.25 spread U.S. 5-year dollar swap 7.50 -0.25 spread U.S. 10-year dollar swap 0.75 0.00 spread U.S. 30-year dollar swap -26.50 0.50 spread (Reporting by Karen Pierog in Chicago and Gertrude Chavez-Dreyfuss in New York, Editing by Nick Zieminski and Sonya Hepinstall)