(Updates throughout; adds analyst comments, upcoming ADP report, and reverse repo volume) By Karen Pierog CHICAGO, June 29 (Reuters) - U.S. Treasury yields hugged the unchanged mark on Tuesday as the market waited to see how June U.S. employment data, due later this week, might affect the Federal Reserve"s monetary policy stance. The benchmark 10-year yield, which rose as high as 1.51% earlier in the session, was last flat at 1.4782%. "We"re sitting in a little bit of consolidation range on a technical level," said Ellis Phifer, managing director in fixed income research at Raymond James, noting "the calm before the potential storm" that the closely watched nonfarm payrolls report due out Friday could bring. Ahead of the U.S. Labor Department"s data, Wednesday"s ADP National Employment Report is expected to show private payrolls rose by 600,000 in June, after surging by 978,000 in May. While the ADP report is at times not a good predictor of the government"s data, it will still be watched by the market, particularly if there are any substantial revisions to its May numbers, said Andrew Richman, senior fixed income strategist at Sterling Capital Management. A clearer picture of the jobs market, a key focus of the Fed, will emerge in the coming months when enhanced unemployment benefits end and students head back to classrooms, freeing parents to return to work, said Bill Merz, chief fixed income strategist at U.S. Bank Wealth Management. He cited many unknowns regarding the speed and magnitude of the Fed"s easing of the accommodative policies put in place last year to aid the coronavirus-battered economy. "The bottom line is that we"re all macro investors now and the macro picture is cloudy," Merz said, noting concerns about how much the economy can be tightened even as the flood of stimulus continues. Richmond Fed President Thomas Barkin said on Tuesday he would be ready to start tapering the central bank"s $120 billion in monthly asset purchases as soon as "substantial further progress" on employment has been met. Meanwhile, the amount of cash flowing into the Fed"s overnight reverse repurchase operation hit a record high $841.2 billion on Tuesday. While volume has been building since March, it grew further after the Fed earlier this month raised the rate it pays on reverse repurchase agreements to 0.05% from 0% as part of technical adjustments to keep the effective federal funds rate from falling too low. The two-year Treasury yield was last less than a basis point lower at 0.2524%. A closely watched part of the yield curve that measures the gap between yields on two- and 10-year Treasury notes was last less than a basis point steeper at 122.58 basis points. June 29 Tuesday 3:10PM New York / 1910 GMT Price Current Net Yield % Change (bps) Three-month bills 0.05 0.0507 -0.002 Six-month bills 0.055 0.0558 -0.002 Two-year note 99-191/256 0.2524 -0.004 Three-year note 99-98/256 0.4602 0.000 Five-year note 99-236/256 0.891 -0.003 Seven-year note 100-12/256 1.243 -0.001 10-year note 101-88/256 1.4782 0.000 20-year bond 103-160/256 2.0274 -0.004 30-year bond 106-56/256 2.0939 -0.004 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 7.75 0.25 spread U.S. 3-year dollar swap 11.00 0.50 spread U.S. 5-year dollar swap 7.00 0.25 spread U.S. 10-year dollar swap -2.75 0.75 spread U.S. 30-year dollar swap -31.00 1.00 spread (Reporting by Karen Pierog; Editing by Paul Simao and Richard Chang) Our Standards: The Thomson Reuters Trust Principles.