WASHINGTON (Reuters) - U.S. Republicans are expected to unveil a new infrastructure proposal as early as Tuesday as optimism grows about a possible bipartisan deal that would cover a fraction of President Joe Biden’s $2.3 trillion infrastructure plan. Senator Shelley Moore Capito, who is leading the Republican infrastructure drive, told reporters on Monday that she expected Republicans to unveil a new counter-proposal to Biden’s sweeping plan sometime early this week. Her comments followed a day of discussions between Senate Republicans and White House staff, on the eve of a meeting with top administration officials slated for Tuesday afternoon. Capito and other Republicans including Senate Commerce Committee Chairman Roger Wicker announced an initial $568 billion infrastructure plan, which Democrats criticized as inadequate. Capito and Wicker were among a group of Senate Republicans who met with Biden last Thursday. Asked whether Senate Republicans would unveil a new infrastructure proposal on Tuesday, Capito replied: “We hope so. Well, it’ll be early this week.” She offered no details. But Republicans including Senate Minority Leader Mitch McConnell have signaled a willingness to consider a proposal closer to $600 billion, while a bipartisan group of senators has discussed a package of roughly $1 trillion. Capito, Wicker and fellow Senate Republicans John Barrasso, Roy Blunt, Mike Crapo and Pat Toomey were due to meet with senior administration officials, including Transportation Secretary Pete Buttigieg and Commerce Secretary Gina Raimondo, in the Capitol on Tuesday. “I think all four of the committees involved are making a good-faith effort to try to get to a good offer. We all would like to see a big infrastructure package,” Blunt told reporters on Monday. Biden’s mammoth infrastructure proposal includes traditional projects to revitalize roads and bridges, but would also seek to address climate change and social issues such as elder care. The president said he would pay for the plan by raising taxes on U.S. corporations. Republican have rejected Biden’s proposal as too broad and too expensive, and instead have sought to reach a bipartisan deal that focuses on roads, bridges, waterways and broadband access. Democrats have floated a two-track approach that would include a smaller bipartisan package, as well as more sweeping legislation that they could enact without Republican support through a process known as reconciliation. Reporting by David Morgan; Editing by Bill Berkrot Our Standards: The Thomson Reuters Trust Principles.