Negotiations with Joe Biden over a potentially massive infrastructure investment package are inching forward even though disagreements remain over the size and scope of such legislation, Republican senator Shelley Moore Capito said on Sunday. “I think we can get to real compromise, absolutely, because we’re both still in the game,” Capito told Fox News Sunday. Capito leads a group of six Republicans in regular contact with Biden and White House aides over a bill the administration wants to move through Congress promptly. The Republicans have proposed $928bn to improve roads, bridges and other traditional infrastructure projects. Much of the funding would come from money already enacted into law for other purposes. The administration’s latest offer in negotiations is for $1.7tn and would include spending on projects that go beyond traditional infrastructure, such as homecare for the elderly. The transportation secretary, Pete Buttigieg, told ABC’s This Week: “There’s movement in the right direction, but a lot of concern … We need to make investments over and above what would have happened anyway.” He also highlighted the need for using the infrastructure bill to address climate change and indicated opposition to shifting Covid-19 relief money to infrastructure accounts. Capito said that following a White House meeting which Republicans viewed as productive, Biden aides stepped away from some ideas Republicans pushed. “We have had some back and forth with the staff that sort of pulled back a little bit but I think we’re smoothing out those edges,” said the West Virginia senator, whose state stands to benefit significantly from infrastructure investment. Republicans continued to balk at raising taxes on the wealthy and corporations to help finance the projects. “I’m not going to vote to overturn those,” Capito said when asked about rolling back some tax cuts enacted during the Trump administration. She also held the line against including new funding for projects that go beyond physical infrastructure, saying those could be considered in other measures. Talks are expected to continue this week even though Congress is on a break, with the Senate returning on 7 June. When lawmakers return to Washington, Biden will be under pressure from Democrats to sidestep Republicans if talks do not show signs of significant progress. Buttigieg told CNN’s State of the Union there needed to be a clear direction on the infrastructure bill. “The president keeps saying ‘Inaction is not an option’ and time is not unlimited here,” he said. The New York Democratic senator Kirsten Gillibrand told CNN: “I think waiting any longer for Republicans to do the right thing is a misstep … I would go forward.” The Senate could use the “reconciliation” process that requires only a simple majority to advance legislation, instead of the usual 60-vote threshold. The Senate is split 50-50 with Vice-President Kamala Harris having the power to break deadlocks. It is not clear if all Democrats would go along with such a process.