Mr Hatch said he and fellow Republican Paul Ryan, chairman of the House Ways and Means Committee, were having some success convincing some tea party Republicans. He also praised Mr Obama for taking on his critics in the Democratic party more forcefully in recent weeks.
But the president and his Republican allies on the issue still faced a tough fight, Mr Hatch said.
“This is one thing where the president is right and you would think Democrats would help him to have this big victory,” the senator said. “It would be the most important victory for the president in his whole eight years.”
Democratic opponents “are going to throw bombs in the Senate when we bring it up”, he said. “[The president has] got to work to get more Democrats on board.”